This paper deals with the existence of weak solutions of the system that describes the two‐phase two‐component fluid flow in porous media. Both two‐phase and possible one‐phase flow regions are taken into account. Our research is based on a global pressure, an artificial variable that allows us to partially decouple the original equations. As a second primary unknown for the system, we choose the gas pseudo‐pressure, a persistent variable which coincides with the gas pressure in the two‐phase regions while it does not have physical meaning in one‐phase flow regions, when only the liquid phase is present. This allows us to introduce an another persistent variable that is an artificial variable in one‐phase flow regions and a physical variable in two‐phase flow regions—the capillary pseudopressure. We rewrite the system's equations in a fully equivalent form in terms of the global pressure and the gas‐pseudo pressure. In order to prove the existence of weak solutions of obtained system, we also use the capillary pseudo‐pressure. By using it, we can decouple obtained equations on the discrete level. This allows us to derive the existence result for weak solutions in more tractable way.
{"title":"Mathematical analysis of the two‐phase two‐component fluid flow in porous media by an artificial persistent variables approach","authors":"Anja Vrbaški, Ana Žgaljić Keko","doi":"10.1002/mma.10454","DOIUrl":"https://doi.org/10.1002/mma.10454","url":null,"abstract":"This paper deals with the existence of weak solutions of the system that describes the two‐phase two‐component fluid flow in porous media. Both two‐phase and possible one‐phase flow regions are taken into account. Our research is based on a global pressure, an artificial variable that allows us to partially decouple the original equations. As a second primary unknown for the system, we choose the gas pseudo‐pressure, a persistent variable which coincides with the gas pressure in the two‐phase regions while it does not have physical meaning in one‐phase flow regions, when only the liquid phase is present. This allows us to introduce an another persistent variable that is an artificial variable in one‐phase flow regions and a physical variable in two‐phase flow regions—the capillary pseudopressure. We rewrite the system's equations in a fully equivalent form in terms of the global pressure and the gas‐pseudo pressure. In order to prove the existence of weak solutions of obtained system, we also use the capillary pseudo‐pressure. By using it, we can decouple obtained equations on the discrete level. This allows us to derive the existence result for weak solutions in more tractable way.","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220252","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Elvio Accinelli, Atefeh Afsar, Filipe Martins, José Martins, Bruno M.P.M. Oliveira, Jorge Oviedo, Alberto A. Pinto, Luis Quintas
This paper fits in the theory of international agreements by studying the success of stable coalitions of agents seeking the preservation of a public good. Extending Baliga and Maskin, we consider a model of homogeneous agents with quasi‐linear utilities of the form , where is the aggregate contribution and the exponent is the elasticity of the gross utility. When the value of the elasticity increases in its natural range , we prove the following five main results in the formation of stable coalitions: (i) the gap of cooperation, characterized as the ratio of the welfare of the grand coalition to the welfare of the competitive singleton coalition grows to infinity, which we interpret as a measure of the urge or need to save the public good; (ii) the size of stable coalitions increases from 1 up to ; (iii) the ratio of the welfare of stable coalitions to the welfare of the competitive singleton coalition grows to infinity; (iv) the ratio of the welfare of stable coalitions to the welfare of the grand coalition “decreases” (a lot), up to when the number of members of the stable coalition is approximately and after that it “increases” (a lot); and (v) the growth of stable coalitions occurs with a much greater loss of the coalition members when compared with free‐riders. Result (v) has two major drawbacks: (a) A priori, it is difficult to “convince” agents to be members of the stable coalition and (b) together with results (i) and (iv), it explains and leads to the “pessimistic” Barrett's paradox of cooperation, even in a case not much considered in the literature: The ratio of the welfare of the stable coalitions against the welfare of the grand coalition is small, even in the extreme case where there are few (or a single) free‐riders and the gap of cooperation is large. “Optimistically,” result (iii) shows that stable coalitions do much better than the competitive singleton coalition. Furthermore, result (ii) proves that the paradox of cooperation is resolved for larger values of so that the grand coalition is stabilized.
{"title":"Barrett's paradox of cooperation in the case of quasi‐linear utilities","authors":"Elvio Accinelli, Atefeh Afsar, Filipe Martins, José Martins, Bruno M.P.M. Oliveira, Jorge Oviedo, Alberto A. Pinto, Luis Quintas","doi":"10.1002/mma.10447","DOIUrl":"https://doi.org/10.1002/mma.10447","url":null,"abstract":"This paper fits in the theory of international agreements by studying the success of stable coalitions of agents seeking the preservation of a public good. Extending Baliga and Maskin, we consider a model of homogeneous agents with quasi‐linear utilities of the form , where is the aggregate contribution and the exponent is the elasticity of the gross utility. When the value of the elasticity increases in its natural range , we prove the following five main results in the formation of stable coalitions: (i) the gap of cooperation, characterized as the ratio of the welfare of the grand coalition to the welfare of the competitive singleton coalition grows to infinity, which we interpret as a measure of the urge or need to save the public good; (ii) the size of stable coalitions increases from 1 up to ; (iii) the ratio of the welfare of stable coalitions to the welfare of the competitive singleton coalition grows to infinity; (iv) the ratio of the welfare of stable coalitions to the welfare of the grand coalition “decreases” (a lot), up to when the number of members of the stable coalition is approximately and after that it “increases” (a lot); and (v) the growth of stable coalitions occurs with a much greater loss of the coalition members when compared with free‐riders. Result (v) has two major drawbacks: (a) <jats:italic>A priori</jats:italic>, it is difficult to “convince” agents to be members of the stable coalition and (b) together with results (i) and (iv), it explains and leads to the “pessimistic” Barrett's paradox of cooperation, even in a case not much considered in the literature: The ratio of the welfare of the stable coalitions against the welfare of the grand coalition is small, even in the extreme case where there are few (or a single) free‐riders and the gap of cooperation is large. “Optimistically,” result (iii) shows that stable coalitions do much better than the competitive singleton coalition. Furthermore, result (ii) proves that the paradox of cooperation is resolved for larger values of so that the grand coalition is stabilized.","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220247","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We consider the Ricker model with delay and constant or periodic stocking. We found that the high stocking density tends to neutralize the delay effect on stability. Conditions are established on the parameters to ensure the global stability of the equilibrium solution in the case of constant stocking, as well as the global stability of the 2‐periodic solution in the case of 2‐periodic stocking. Our approach extensively relies on the utilization of the embedding technique. Whether constant stocking or periodic stocking, the model has the potential to undergo a Neimark–Sacker bifurcation in both cases. However, the Neimark–Sacker bifurcation in the 2‐periodic case results in the emergence of two invariant curves that collectively function as a single attractor. Finally, we pose open questions in the form of conjectures about global stability for certain choices of the parameters.
{"title":"Global stability in the Ricker model with delay and stocking","authors":"Ziyad AlSharawi, Sadok Kallel","doi":"10.1002/mma.10440","DOIUrl":"https://doi.org/10.1002/mma.10440","url":null,"abstract":"We consider the Ricker model with delay and constant or periodic stocking. We found that the high stocking density tends to neutralize the delay effect on stability. Conditions are established on the parameters to ensure the global stability of the equilibrium solution in the case of constant stocking, as well as the global stability of the 2‐periodic solution in the case of 2‐periodic stocking. Our approach extensively relies on the utilization of the embedding technique. Whether constant stocking or periodic stocking, the model has the potential to undergo a Neimark–Sacker bifurcation in both cases. However, the Neimark–Sacker bifurcation in the 2‐periodic case results in the emergence of two invariant curves that collectively function as a single attractor. Finally, we pose open questions in the form of conjectures about global stability for certain choices of the parameters.","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220255","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Akbar Zada, Usman Riaz, Junaid Jamshed, Mehboob Alam, Afef Kallekh
The main focus of this manuscript is to study an impulsive fractional integro‐differential equation with delay and Caputo fractional derivative. The existence solution of such a class of fractional differential equations is discussed for linear and nonlinear case with the help of direct integral method. Moreover, Banach's fixed point theorem and Schaefer's fixed point theorem are use to discuss the uniqueness and at least one solution of the said fractional differential equations, respectively. Some hypothesis and inequalities are utilize to present four different types of Hyers–Ulam stability of the mentioned impulsive integro‐differential equation. Example is provide for the illustration of main results.
{"title":"Analysis of impulsive Caputo fractional integro‐differential equations with delay","authors":"Akbar Zada, Usman Riaz, Junaid Jamshed, Mehboob Alam, Afef Kallekh","doi":"10.1002/mma.10426","DOIUrl":"https://doi.org/10.1002/mma.10426","url":null,"abstract":"The main focus of this manuscript is to study an impulsive fractional integro‐differential equation with delay and Caputo fractional derivative. The existence solution of such a class of fractional differential equations is discussed for linear and nonlinear case with the help of direct integral method. Moreover, Banach's fixed point theorem and Schaefer's fixed point theorem are use to discuss the uniqueness and at least one solution of the said fractional differential equations, respectively. Some hypothesis and inequalities are utilize to present four different types of Hyers–Ulam stability of the mentioned impulsive integro‐differential equation. Example is provide for the illustration of main results.","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220251","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this study, a wavelet‐based collocation scheme has been introduced for solving the linear and nonlinear Fredholm integral equations as well as the system of linear Fredholm integral equations with weakly singular logarithmic kernel. Initially, Laguerre wavelets have been constructed by dilation and translation of Laguerre polynomials. For the numerical solution of the Fredholm integral equations, all the functions have been approximated with respect to the Laguerre wavelets. Then, the proposed linear and nonlinear Fredholm integral equations reduce to systems of linear and nonlinear algebraic equations by utilizing the function approximations. Furthermore, the error estimation and the convergence analysis of the presented method have been discussed. Moreover, the numerical results of the several experiments have also been presented in both graphical and tabular form to describe the accuracy and efficiency of the approached method, and also, to determine the validity of the presented scheme, the approximate solutions and absolute error values are compared with the results obtained by other existing approaches.
{"title":"A new Laguerre wavelets‐based method for solving Fredholm integral equations with weakly singular logarithmic kernel","authors":"Srikanta Behera, Santanu Saha Ray","doi":"10.1002/mma.10405","DOIUrl":"https://doi.org/10.1002/mma.10405","url":null,"abstract":"In this study, a wavelet‐based collocation scheme has been introduced for solving the linear and nonlinear Fredholm integral equations as well as the system of linear Fredholm integral equations with weakly singular logarithmic kernel. Initially, Laguerre wavelets have been constructed by dilation and translation of Laguerre polynomials. For the numerical solution of the Fredholm integral equations, all the functions have been approximated with respect to the Laguerre wavelets. Then, the proposed linear and nonlinear Fredholm integral equations reduce to systems of linear and nonlinear algebraic equations by utilizing the function approximations. Furthermore, the error estimation and the convergence analysis of the presented method have been discussed. Moreover, the numerical results of the several experiments have also been presented in both graphical and tabular form to describe the accuracy and efficiency of the approached method, and also, to determine the validity of the presented scheme, the approximate solutions and absolute error values are compared with the results obtained by other existing approaches.","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220253","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper investigates an optimal investment‐reinsurance problem for an insurer who possesses inside information regarding the future realizations of the claim process and risky asset process. The insurer sells insurance contracts, has access to proportional reinsurance business, and invests in a financial market consisting of three assets: one risk‐free asset, one bond, and one stock. Here, the nominal interest rate is characterized by the Vasicek model, and the stock price is driven by Heston's stochastic volatility model. Applying the enlargement of filtration techniques, we establish the optimal control problem in which an insurer maximizes the expected power utility of the terminal wealth. By using the dynamic programming principle, the problem can be changed to four‐dimensional Hamilton–Jacobi–Bellman equation. In addition, we adopt a deep neural network method by which the partial differential equation is converted to two backward stochastic differential equations and solved by a stochastic gradient descent‐type optimization procedure. Numerical results obtained using TensorFlow in Python and the economic behavior of the approximate optimal strategy and the approximate optimal utility of the insurer are analyzed.
{"title":"Deep learning solution of optimal reinsurance‐investment strategies with inside information and multiple risks","authors":"Fanyi Peng, Ming Yan, Shuhua Zhang","doi":"10.1002/mma.10465","DOIUrl":"https://doi.org/10.1002/mma.10465","url":null,"abstract":"This paper investigates an optimal investment‐reinsurance problem for an insurer who possesses inside information regarding the future realizations of the claim process and risky asset process. The insurer sells insurance contracts, has access to proportional reinsurance business, and invests in a financial market consisting of three assets: one risk‐free asset, one bond, and one stock. Here, the nominal interest rate is characterized by the Vasicek model, and the stock price is driven by Heston's stochastic volatility model. Applying the enlargement of filtration techniques, we establish the optimal control problem in which an insurer maximizes the expected power utility of the terminal wealth. By using the dynamic programming principle, the problem can be changed to four‐dimensional Hamilton–Jacobi–Bellman equation. In addition, we adopt a deep neural network method by which the partial differential equation is converted to two backward stochastic differential equations and solved by a stochastic gradient descent‐type optimization procedure. Numerical results obtained using TensorFlow in Python and the economic behavior of the approximate optimal strategy and the approximate optimal utility of the insurer are analyzed.","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220249","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Suliadi Firdaus Sufahani, Wan Noor Afifah Wan Ahmad, Kavikumar Jacob, Sharidan Shafie, Ruzairi Abdul Rahim, Mahmod Abd Hakim Mohamad, Mohd Saifullah Rusiman, Rozaini Roslan, Mohd Zulariffin Md Maarof, Muhamad Ali Imran Kamarudin
This paper considers a non‐standard Optimal Control problem that has an application in economics. The primary focus of this research is to solve the royalty problem, which has been categorized as a non‐standard Optimal Control problem, where the final state value and its functional performance index value are unknown. A new continuous necessary condition is investigated for the final state value so that it will convert the final costate value into a non‐zero value. The research analyzes the seven‐stage royalty piecewise function, which is then approximated to continuous form with the help of the hyperbolic tangent function and solves the problem by using a new modified shooting method. This modified shooting method applies Sufahani–Ahmad–Newton–Brent–Royalty Algorithm and Sufahani‐Ahmad‐Powell‐Brent‐Royalty Algorithm. For a validation process, the results are compared with the existing methods such as Euler, Runge–Kutta, Trapezoidal, and Hermite–Simpson approximations, and the results show that the proposed method yields an accurate terminal state value.
{"title":"Solving a non‐standard Optimal Control royalty payment problem using a new modified shooting method","authors":"Suliadi Firdaus Sufahani, Wan Noor Afifah Wan Ahmad, Kavikumar Jacob, Sharidan Shafie, Ruzairi Abdul Rahim, Mahmod Abd Hakim Mohamad, Mohd Saifullah Rusiman, Rozaini Roslan, Mohd Zulariffin Md Maarof, Muhamad Ali Imran Kamarudin","doi":"10.1002/mma.10457","DOIUrl":"https://doi.org/10.1002/mma.10457","url":null,"abstract":"This paper considers a non‐standard Optimal Control problem that has an application in economics. The primary focus of this research is to solve the royalty problem, which has been categorized as a non‐standard Optimal Control problem, where the final state value and its functional performance index value are unknown. A new continuous necessary condition is investigated for the final state value so that it will convert the final costate value into a non‐zero value. The research analyzes the seven‐stage royalty piecewise function, which is then approximated to continuous form with the help of the hyperbolic tangent function and solves the problem by using a new modified shooting method. This modified shooting method applies Sufahani–Ahmad–Newton–Brent–Royalty Algorithm and Sufahani‐Ahmad‐Powell‐Brent‐Royalty Algorithm. For a validation process, the results are compared with the existing methods such as Euler, Runge–Kutta, Trapezoidal, and Hermite–Simpson approximations, and the results show that the proposed method yields an accurate terminal state value.","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220250","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we investigate the following fractional Kirchhoff‐type pseudo parabolic equation driven by a nonlocal integro‐differential operator : where represents the Gagliardo seminorm of . Instead of imposing specific assumptions on the Kirchhoff function, we introduce a more general sense to establish the local existence of weak solutions. Moreover, via the sharp fractional Hardy inequality, the decay estimates for global weak solutions, the blow‐up criterion, blow‐up rate, and the upper and lower bounds of the blow‐up time are derived. Lastly, we discuss the global existence and finite time blow‐up results with high initial energy.
{"title":"A nonlocal Kirchhoff diffusion problem with singular potential and logarithmic nonlinearity","authors":"Zhong Tan, Yi Yang","doi":"10.1002/mma.10451","DOIUrl":"https://doi.org/10.1002/mma.10451","url":null,"abstract":"In this paper, we investigate the following fractional Kirchhoff‐type pseudo parabolic equation driven by a nonlocal integro‐differential operator : <jats:disp-formula> </jats:disp-formula>where represents the Gagliardo seminorm of . Instead of imposing specific assumptions on the Kirchhoff function, we introduce a more general sense to establish the local existence of weak solutions. Moreover, via the sharp fractional Hardy inequality, the decay estimates for global weak solutions, the blow‐up criterion, blow‐up rate, and the upper and lower bounds of the blow‐up time are derived. Lastly, we discuss the global existence and finite time blow‐up results with high initial energy.","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220065","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper explores an inverse problem pertaining to the determination of a source function in non‐divergence parabolic equations, where the solution is known at a discrete set of points. Being different from other ordinary inverse source problems, which are often dependent on only one variable, the unknown coefficient in this paper not only depends on the space variable but also depends on the time . On the basis of the optimal control framework, the existence of the optimal solution of the control function is proved. The necessary conditions to be satisfied by the optimal solution are given. The convergence of the optimal solution when the mesh parameters tend to zero is obtained. The conjugate gradient method is applied to the inverse problem and some numerical results are presented for various typical test examples.
{"title":"Inverse problem of reconstructing source term for a class of non‐divergence parabolic equations","authors":"Xu‐Wei Tie, Zui‐Cha Deng","doi":"10.1002/mma.10461","DOIUrl":"https://doi.org/10.1002/mma.10461","url":null,"abstract":"This paper explores an inverse problem pertaining to the determination of a source function in non‐divergence parabolic equations, where the solution is known at a discrete set of points. Being different from other ordinary inverse source problems, which are often dependent on only one variable, the unknown coefficient in this paper not only depends on the space variable but also depends on the time . On the basis of the optimal control framework, the existence of the optimal solution of the control function is proved. The necessary conditions to be satisfied by the optimal solution are given. The convergence of the optimal solution when the mesh parameters tend to zero is obtained. The conjugate gradient method is applied to the inverse problem and some numerical results are presented for various typical test examples.","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220254","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Muneera Abdullah Qadha, Sarah Abdullah Qadha, Ahmed Bakhet
In this paper, our aim is to introduce a new definition of ( ‐incomplete Wright hypergeometric matrix functions ( ‐IWHMFs) using the ‐incomplete Pochhammer matrix symbol. First, we define the ‐incomplete gamma matrix function and introduce the ‐incomplete Pochhammer matrix symbols. Furthermore, we present differential formulas and integral representation related to these ‐IWHMFs. We have also obtained some results regarding the ‐fractional calculus operators of these ‐IWHMFs. Finally, we investigate the solutions of fractional kinetic equations (FKEs) involving the ‐IWHMFs.
{"title":"On the matrix versions of the k analog of ℑ‐incomplete Gauss hypergeometric functions and associated fractional calculus","authors":"Muneera Abdullah Qadha, Sarah Abdullah Qadha, Ahmed Bakhet","doi":"10.1002/mma.10382","DOIUrl":"https://doi.org/10.1002/mma.10382","url":null,"abstract":"In this paper, our aim is to introduce a new definition of ( ‐incomplete Wright hypergeometric matrix functions ( ‐IWHMFs) using the ‐incomplete Pochhammer matrix symbol. First, we define the ‐incomplete gamma matrix function and introduce the ‐incomplete Pochhammer matrix symbols. Furthermore, we present differential formulas and integral representation related to these ‐IWHMFs. We have also obtained some results regarding the ‐fractional calculus operators of these ‐IWHMFs. Finally, we investigate the solutions of fractional kinetic equations (FKEs) involving the ‐IWHMFs.","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220043","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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