Pub Date : 2023-03-14DOI: 10.1109/ICFDA58234.2023.10153180
I. Batiha, Noureddine Djenina, A. Ouannas, Taki-Eddine Oussaeif, L. B. Aoua, S. Momani
The mathematical study of the growth of a cancer tumor gives us great progress in knowing the behavior of the cancer tumor as well as taking appropriate therapeutic measures. In this article, we endeavor to investigate a mathematical model of a cancer tumor and study its stabilization. In particular, we first discritize the continuous model connected with the dynamics of cancer tumor to get the discrete model. Then we perform several numerical simulations that will show that the proposed discrete model can behave chaotically. As a result, we study the unique fixed point stability that has a physical meaning, and finally we controlled the proposed system to stabilized its dynamics at such a point.
{"title":"Control of chaos in incommensurate fractional order discrete system","authors":"I. Batiha, Noureddine Djenina, A. Ouannas, Taki-Eddine Oussaeif, L. B. Aoua, S. Momani","doi":"10.1109/ICFDA58234.2023.10153180","DOIUrl":"https://doi.org/10.1109/ICFDA58234.2023.10153180","url":null,"abstract":"The mathematical study of the growth of a cancer tumor gives us great progress in knowing the behavior of the cancer tumor as well as taking appropriate therapeutic measures. In this article, we endeavor to investigate a mathematical model of a cancer tumor and study its stabilization. In particular, we first discritize the continuous model connected with the dynamics of cancer tumor to get the discrete model. Then we perform several numerical simulations that will show that the proposed discrete model can behave chaotically. As a result, we study the unique fixed point stability that has a physical meaning, and finally we controlled the proposed system to stabilized its dynamics at such a point.","PeriodicalId":381521,"journal":{"name":"2023 International Conference on Fractional Differentiation and Its Applications (ICFDA)","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126606420","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-03-14DOI: 10.1109/ICFDA58234.2023.10153326
Ammar Abuualshaikh, F. Abdullah, M. Akbar
In this paper, the New Generalized Differential Transform Method (NGDTM) is exploited to present an analytical solution for the fractional order Riccati Differential Equation, taking into account the Riemann-Liouville type fractional derivatives. Three different problems with multiple $beta$ values were solved using this technique, and the solutions were compared very well with those obtained by exact solutions.
{"title":"Application of New Generalized Differential Transform Method to Solve Riccati Fractional Differential Equation","authors":"Ammar Abuualshaikh, F. Abdullah, M. Akbar","doi":"10.1109/ICFDA58234.2023.10153326","DOIUrl":"https://doi.org/10.1109/ICFDA58234.2023.10153326","url":null,"abstract":"In this paper, the New Generalized Differential Transform Method (NGDTM) is exploited to present an analytical solution for the fractional order Riccati Differential Equation, taking into account the Riemann-Liouville type fractional derivatives. Three different problems with multiple $beta$ values were solved using this technique, and the solutions were compared very well with those obtained by exact solutions.","PeriodicalId":381521,"journal":{"name":"2023 International Conference on Fractional Differentiation and Its Applications (ICFDA)","volume":"140 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116433378","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-03-14DOI: 10.1109/ICFDA58234.2023.10153199
Mamta Kapoor, Samanyu Khosla
The present paper discusses an iterative technique involving the use of Yang transform to obtain series solution to fractional Klein Gordon equation. A few preliminaries involving Yang transform are provided. Tables for Yang and inverse Yang transform of common functions have been provided. The general formula for the technique is developed and an example is solved using the method to illustrate its efficacy. The obtained series solution is used to generate graphs with varying values of the fractional order and are thus used to show the behavior of the example used within the bounds considered in the graphs. Concluding remarks are provided.
{"title":"An iterative technique using Yang transform to solve fractional order Klein Gordon equation","authors":"Mamta Kapoor, Samanyu Khosla","doi":"10.1109/ICFDA58234.2023.10153199","DOIUrl":"https://doi.org/10.1109/ICFDA58234.2023.10153199","url":null,"abstract":"The present paper discusses an iterative technique involving the use of Yang transform to obtain series solution to fractional Klein Gordon equation. A few preliminaries involving Yang transform are provided. Tables for Yang and inverse Yang transform of common functions have been provided. The general formula for the technique is developed and an example is solved using the method to illustrate its efficacy. The obtained series solution is used to generate graphs with varying values of the fractional order and are thus used to show the behavior of the example used within the bounds considered in the graphs. Concluding remarks are provided.","PeriodicalId":381521,"journal":{"name":"2023 International Conference on Fractional Differentiation and Its Applications (ICFDA)","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116451088","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-03-14DOI: 10.1109/ICFDA58234.2023.10153241
Muhammad Farman, D. Baleanu
Despite the existence of a secure environment, smoke subjection continues to be a leading cause of serious illness globally. For investigation and observation of the dynamical transmission of the smoker, we examine a fractional order smoker model with Constant Proportional Atangana-Baleanu (in Caputo sense) operator. We treated the proposed model’s positivity, boundedness, well-posedness and stability analysis of the model. There is a brief discussion of additional analysis on CPABC operators. Using the Laplace Adomian Decomposition Method, we simulate a system of fractional differential equations numerically. This model’s tools seem to be quite strong and capable of reproducing the issue’s anticipated theoretical conditions.
{"title":"Modeling and Analysis of Smokers Model with Constant Proportional Fractional Operators","authors":"Muhammad Farman, D. Baleanu","doi":"10.1109/ICFDA58234.2023.10153241","DOIUrl":"https://doi.org/10.1109/ICFDA58234.2023.10153241","url":null,"abstract":"Despite the existence of a secure environment, smoke subjection continues to be a leading cause of serious illness globally. For investigation and observation of the dynamical transmission of the smoker, we examine a fractional order smoker model with Constant Proportional Atangana-Baleanu (in Caputo sense) operator. We treated the proposed model’s positivity, boundedness, well-posedness and stability analysis of the model. There is a brief discussion of additional analysis on CPABC operators. Using the Laplace Adomian Decomposition Method, we simulate a system of fractional differential equations numerically. This model’s tools seem to be quite strong and capable of reproducing the issue’s anticipated theoretical conditions.","PeriodicalId":381521,"journal":{"name":"2023 International Conference on Fractional Differentiation and Its Applications (ICFDA)","volume":"54 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122679032","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-03-14DOI: 10.1109/ICFDA58234.2023.10153214
Manal Almuzini, I. Batiha, S. Momani
In more recent times, many monkeypox disease cases have steadily increased and the range of the projected outbreaks in human populations has grown constantly. In the light of these aspects, this work proposes a new fractional-order version for one of the Susceptible-Exposed-Infectious-Recovered models (or simply SEIR models). This model, which is formulated in the sense of Caputo fractional differentiator, is first analyzed in terms of finding some theoretical results related to the stability analysis and the basic reproduction number. Then, with the help of using a novel recent version of the fractional Euler method, called Fractional Modified Euler Method (FMEM), the proposed model is solved numerically. Several numerical simulations are presented afterward for completeness.
{"title":"A study of fractional-order monkeypox mathematical model with its stability analysis","authors":"Manal Almuzini, I. Batiha, S. Momani","doi":"10.1109/ICFDA58234.2023.10153214","DOIUrl":"https://doi.org/10.1109/ICFDA58234.2023.10153214","url":null,"abstract":"In more recent times, many monkeypox disease cases have steadily increased and the range of the projected outbreaks in human populations has grown constantly. In the light of these aspects, this work proposes a new fractional-order version for one of the Susceptible-Exposed-Infectious-Recovered models (or simply SEIR models). This model, which is formulated in the sense of Caputo fractional differentiator, is first analyzed in terms of finding some theoretical results related to the stability analysis and the basic reproduction number. Then, with the help of using a novel recent version of the fractional Euler method, called Fractional Modified Euler Method (FMEM), the proposed model is solved numerically. Several numerical simulations are presented afterward for completeness.","PeriodicalId":381521,"journal":{"name":"2023 International Conference on Fractional Differentiation and Its Applications (ICFDA)","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114269140","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-03-14DOI: 10.1109/ICFDA58234.2023.10153300
Ali Ma’Bdeh, N. Tawalbeh, R. El-Khazali
The rotor position and speed of synchronous motors are required in vector control applications to achieve efficient performance of such motors. Many methods of sensorless speed control of a permanent-magnet synchronous motor (PMSM) have been developed to overcome the limitations of sensors. This work introduces a new sensorless speed controller of PMSM using fractional-order extended state observer (FoESO). The fractionalorder dynamics of the extended state observer provide better performance and higher estimation accuracy than the integer-order one. The performance of the proposed model is validated via numerical simulations by using two distinct realizations for the FoESO; namely, Oustaloup’s, and El-Khazalis’ approximations. Besides its lowest order, El-Khazali’s first-order approximation provides a competitive candidate to that of other approximations of higher orders. All results are demonstrated via numerical simulation.
{"title":"Sensorless Speed Control of a PMSM Using Fractional-Order Extended State Observer","authors":"Ali Ma’Bdeh, N. Tawalbeh, R. El-Khazali","doi":"10.1109/ICFDA58234.2023.10153300","DOIUrl":"https://doi.org/10.1109/ICFDA58234.2023.10153300","url":null,"abstract":"The rotor position and speed of synchronous motors are required in vector control applications to achieve efficient performance of such motors. Many methods of sensorless speed control of a permanent-magnet synchronous motor (PMSM) have been developed to overcome the limitations of sensors. This work introduces a new sensorless speed controller of PMSM using fractional-order extended state observer (FoESO). The fractionalorder dynamics of the extended state observer provide better performance and higher estimation accuracy than the integer-order one. The performance of the proposed model is validated via numerical simulations by using two distinct realizations for the FoESO; namely, Oustaloup’s, and El-Khazalis’ approximations. Besides its lowest order, El-Khazali’s first-order approximation provides a competitive candidate to that of other approximations of higher orders. All results are demonstrated via numerical simulation.","PeriodicalId":381521,"journal":{"name":"2023 International Conference on Fractional Differentiation and Its Applications (ICFDA)","volume":"309 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117010981","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-03-14DOI: 10.1109/ICFDA58234.2023.10153184
Rabia Chaimaà Karoun, A. Ouannas, M. Horani, T. Ziar, I. Batiha, Z. Dibi
In this paper, a three dimensional discrete time Hopfield neural network with commensurate fractional variable order is presented based on the Caputo like difference operator. The dynamics of the proposed system is investigated by means of chaotic attractors, bifurcation diagram and maximum Lyapunov exponents, It is shown that the discrete time Hopfield neural network has complex behaviour for several fractional variable orders and different system parameter values. Moreover, the approximate entropy and the C0 complexity algorithms of the system are performed to prove the existence of chaos. Finally, the corresponding simulations are carried out on Matlab to illustrate the theoretical results.
{"title":"Chaos in The Fractional Variable Order Discrete-Time Neural Networks*","authors":"Rabia Chaimaà Karoun, A. Ouannas, M. Horani, T. Ziar, I. Batiha, Z. Dibi","doi":"10.1109/ICFDA58234.2023.10153184","DOIUrl":"https://doi.org/10.1109/ICFDA58234.2023.10153184","url":null,"abstract":"In this paper, a three dimensional discrete time Hopfield neural network with commensurate fractional variable order is presented based on the Caputo like difference operator. The dynamics of the proposed system is investigated by means of chaotic attractors, bifurcation diagram and maximum Lyapunov exponents, It is shown that the discrete time Hopfield neural network has complex behaviour for several fractional variable orders and different system parameter values. Moreover, the approximate entropy and the C0 complexity algorithms of the system are performed to prove the existence of chaos. Finally, the corresponding simulations are carried out on Matlab to illustrate the theoretical results.","PeriodicalId":381521,"journal":{"name":"2023 International Conference on Fractional Differentiation and Its Applications (ICFDA)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129053240","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-03-14DOI: 10.1109/ICFDA58234.2023.10153172
Maja Jolić, S. Konjik, D. Mitrovic
Motivated by the porous media equation as well as population dynamics models, we study a nonlinear fractional system of differential equations and investigate a control problem for such system. We look for the control that will govern the system from a given initial state to a desired final state. The strategy that will be employed in order to solve the problem is essentially novel and involve various techniques and tools from fractional calculus and functional analysis. The basic idea consists of linearizing the system, and then using the fixed point results to obtain a solution. Also, we are interested in concepts such as controllability and observability in the fractional framework, which further involve the Gramian matrix, the Kalman rank condition and the adjoint system.
{"title":"A New Approach in Solving Fractional Nonlinear Control Problems","authors":"Maja Jolić, S. Konjik, D. Mitrovic","doi":"10.1109/ICFDA58234.2023.10153172","DOIUrl":"https://doi.org/10.1109/ICFDA58234.2023.10153172","url":null,"abstract":"Motivated by the porous media equation as well as population dynamics models, we study a nonlinear fractional system of differential equations and investigate a control problem for such system. We look for the control that will govern the system from a given initial state to a desired final state. The strategy that will be employed in order to solve the problem is essentially novel and involve various techniques and tools from fractional calculus and functional analysis. The basic idea consists of linearizing the system, and then using the fixed point results to obtain a solution. Also, we are interested in concepts such as controllability and observability in the fractional framework, which further involve the Gramian matrix, the Kalman rank condition and the adjoint system.","PeriodicalId":381521,"journal":{"name":"2023 International Conference on Fractional Differentiation and Its Applications (ICFDA)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130586504","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-03-14DOI: 10.1109/ICFDA58234.2023.10153309
P. Lanusse, T. Airimitoaie, Evgeny Shulga, S. Maurel
In order to extend the efficiency of linear fractional order controllers for nonlinear and preview systems, this paper shows how to design an optimal, robust and safe control-system. The robustness and safety of the control-system is achieved with a linear and fractional order feedback controller that takes into account model uncertainties and frequency-domain constraints. Complementary, a nonlinear model-based optimisation is used to design a nominal anticipative feedforward control and reference closed-loop trajectory. The computing time is considered in the implementation.
{"title":"Principles of a safe and high performing CRONE control of nonlinear systems","authors":"P. Lanusse, T. Airimitoaie, Evgeny Shulga, S. Maurel","doi":"10.1109/ICFDA58234.2023.10153309","DOIUrl":"https://doi.org/10.1109/ICFDA58234.2023.10153309","url":null,"abstract":"In order to extend the efficiency of linear fractional order controllers for nonlinear and preview systems, this paper shows how to design an optimal, robust and safe control-system. The robustness and safety of the control-system is achieved with a linear and fractional order feedback controller that takes into account model uncertainties and frequency-domain constraints. Complementary, a nonlinear model-based optimisation is used to design a nominal anticipative feedforward control and reference closed-loop trajectory. The computing time is considered in the implementation.","PeriodicalId":381521,"journal":{"name":"2023 International Conference on Fractional Differentiation and Its Applications (ICFDA)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130664464","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-03-14DOI: 10.1109/ICFDA58234.2023.10153234
A. Kalaiyarasi, S. Devi, V. Raj
A non-linear differential equation of the SIR epidemic model is taken into consideration for dynamic analysis. The discussion of these equations’ approximations is followed by a performance analysis of complexity using machine learning algorithms. By utilising this approach to train the patterns, the error value is reduced. The Euler’s method is used to provide time graphs for various parameter values. An experimental result is given to demonstrate how well the machine learning algorithm works. Finally we investigate and compute the errors of the machine learning algorithms to examine the superiority given to demonstrate the reliability and efficiency.
{"title":"Machine Learning Approach to SIR Mathematical Model","authors":"A. Kalaiyarasi, S. Devi, V. Raj","doi":"10.1109/ICFDA58234.2023.10153234","DOIUrl":"https://doi.org/10.1109/ICFDA58234.2023.10153234","url":null,"abstract":"A non-linear differential equation of the SIR epidemic model is taken into consideration for dynamic analysis. The discussion of these equations’ approximations is followed by a performance analysis of complexity using machine learning algorithms. By utilising this approach to train the patterns, the error value is reduced. The Euler’s method is used to provide time graphs for various parameter values. An experimental result is given to demonstrate how well the machine learning algorithm works. Finally we investigate and compute the errors of the machine learning algorithms to examine the superiority given to demonstrate the reliability and efficiency.","PeriodicalId":381521,"journal":{"name":"2023 International Conference on Fractional Differentiation and Its Applications (ICFDA)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131166609","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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