Pub Date : 2019-12-31DOI: 10.30538/PSRP-OMA2019.0031
M. Mellah, A. Hakem
Global existence, uniqueness, and asymptotic behavior of solution for the Euler-Bernoulli viscoelastic equation Mohamed Mellah1,∗ and Ali Hakem2 1 Faculty of Exact Sciences and Computer Science, Hassiba Benbouali University of Chlef, Chlef Algeria. 2 Laboratory ACEDP, Djillali Liabes University, 22000 Sidi Bel Abbes, Algeria.; hakemali@yahoo.com * Correspondence: m.mellah@univ-chlef.dz Received: 21 April 2019; Accepted: 8 May 2019; Published: 11 May 2019. Abstract: We study the global existence and uniqueness of a solution to an initial boundary value problem for the Euler-Bernoulli viscoelastic equation utt + ∆2u− g1 ∗ ∆2u + g2 ∗ ∆u + ut = 0. Further, the asymptotic behavior of solution is established.
{"title":"Global existence, uniqueness, and asymptotic behavior of solution for the Euler-Bernoulli viscoelastic equation","authors":"M. Mellah, A. Hakem","doi":"10.30538/PSRP-OMA2019.0031","DOIUrl":"https://doi.org/10.30538/PSRP-OMA2019.0031","url":null,"abstract":"Global existence, uniqueness, and asymptotic behavior of solution for the Euler-Bernoulli viscoelastic equation Mohamed Mellah1,∗ and Ali Hakem2 1 Faculty of Exact Sciences and Computer Science, Hassiba Benbouali University of Chlef, Chlef Algeria. 2 Laboratory ACEDP, Djillali Liabes University, 22000 Sidi Bel Abbes, Algeria.; hakemali@yahoo.com * Correspondence: m.mellah@univ-chlef.dz Received: 21 April 2019; Accepted: 8 May 2019; Published: 11 May 2019. Abstract: We study the global existence and uniqueness of a solution to an initial boundary value problem for the Euler-Bernoulli viscoelastic equation utt + ∆2u− g1 ∗ ∆2u + g2 ∗ ∆u + ut = 0. Further, the asymptotic behavior of solution is established.","PeriodicalId":52741,"journal":{"name":"Open Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44290437","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 : 2019-12-31DOI: 10.30538/PSRP-OMA2019.0029
Afif Abdalmonem, Omer Abdalrhman, Hossam Eldeen Mohammed
By using the boundedness results for the commutators of the fractional integral with variable kernel on variable Lebesgue spaces Lp(·)(Rn), the boundedness results are established on variable exponent Herz−Morrey spaces MK̇α,λ q,p(·)(R n).
{"title":"Commutators of fractional integral with variable kernel on variable exponent Herz-Morrey spaces","authors":"Afif Abdalmonem, Omer Abdalrhman, Hossam Eldeen Mohammed","doi":"10.30538/PSRP-OMA2019.0029","DOIUrl":"https://doi.org/10.30538/PSRP-OMA2019.0029","url":null,"abstract":"By using the boundedness results for the commutators of the fractional integral with variable kernel on variable Lebesgue spaces Lp(·)(Rn), the boundedness results are established on variable exponent Herz−Morrey spaces MK̇α,λ q,p(·)(R n).","PeriodicalId":52741,"journal":{"name":"Open Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41751622","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 : 2019-12-31DOI: 10.30538/psrp-oma2019.0038
M. Hasan, M. H. A. Biswas, M. Uddin
With the establishment of 200-mile territorial zone in the Bay of Bengal for most countries having coastlines. The control of fishing in these zones has become highly regulated by these countries concerned. In this sense, fishing in territorial waters can be considered a sole owner fishery problem. If the people of a country are allowed to fish freely in the territorial zones, it can be termed as an open access fishery. In an open access fishery, the exploitation of fishing opportunity is completely uncontrolled. This study deals with the problem of harvesting in the prey-predator fishery model in the open access zones and seeks a plan for prey for sustainable fishing, particularly in Sundarbans ecosystem which is situated in the coastal area of the Bay of Bengal. The positive steady state of both local and global stability has been established. Optimal harvesting strategy is also studied for these purposes.
{"title":"A mathematical model for fish management in the Sundarbans ecosystem","authors":"M. Hasan, M. H. A. Biswas, M. Uddin","doi":"10.30538/psrp-oma2019.0038","DOIUrl":"https://doi.org/10.30538/psrp-oma2019.0038","url":null,"abstract":"With the establishment of 200-mile territorial zone in the Bay of Bengal for most countries having coastlines. The control of fishing in these zones has become highly regulated by these countries concerned. In this sense, fishing in territorial waters can be considered a sole owner fishery problem. If the people of a country are allowed to fish freely in the territorial zones, it can be termed as an open access fishery. In an open access fishery, the exploitation of fishing opportunity is completely uncontrolled. This study deals with the problem of harvesting in the prey-predator fishery model in the open access zones and seeks a plan for prey for sustainable fishing, particularly in Sundarbans ecosystem which is situated in the coastal area of the Bay of Bengal. The positive steady state of both local and global stability has been established. Optimal harvesting strategy is also studied for these purposes.","PeriodicalId":52741,"journal":{"name":"Open Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48988381","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 : 2019-12-31DOI: 10.30538/PSRP-OMA2019.0034
A. E. Baraka, Mohamed Toumlilin
Abstract: In this paper, we study the Cauchy problem of the fractional Navier-Stokes equations with Coriolis force in critical Fourier-Besov-Morrey spaces. By using the Fourier localization argument and the Littlewood-Paley theory, we get a local well-posedness results and global well-posedness results with small initial data belonging to the critical Fourier-Besov-Morrey spaces. Moreover; we prove that the corresponding global solution decays to zero as time goes to infinity, and we give the stability result for global solutions.
{"title":"Uniform well-posedness and stability for fractional Navier-Stokes equations with Coriolis force in critical Fourier-Besov-Morrey spaces","authors":"A. E. Baraka, Mohamed Toumlilin","doi":"10.30538/PSRP-OMA2019.0034","DOIUrl":"https://doi.org/10.30538/PSRP-OMA2019.0034","url":null,"abstract":"Abstract: In this paper, we study the Cauchy problem of the fractional Navier-Stokes equations with Coriolis force in critical Fourier-Besov-Morrey spaces. By using the Fourier localization argument and the Littlewood-Paley theory, we get a local well-posedness results and global well-posedness results with small initial data belonging to the critical Fourier-Besov-Morrey spaces. Moreover; we prove that the corresponding global solution decays to zero as time goes to infinity, and we give the stability result for global solutions.","PeriodicalId":52741,"journal":{"name":"Open Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43849211","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 : 2019-12-31DOI: 10.30538/psrp-oma2019.0042
M. Tahir, G. Zaman, Syed Inayat Ali Shah, S. Muhammad, S. Hussain, M. Ishaq
Abstract: Mathematical modeling of infectious diseases has progressed dramatically over the past four decades and continues to flourish at the nexus of mathematics, epidemiology, and infectious diseases research. Now recognized as a valuable tool, mathematical models are being integrated into the public health decision-making process more than ever before. In this article, a mathematical model of Ebola virus which is named as SEIVR (susceptible, exposed, infected, vaccinated, recovered) model is considered. First, we formulate the model and present the basic properties of the proposed model. Then, basic reproductive number is obtained by using the next-generation matrix approach. Furthermore, the sensitivity analysis of R0 is also discussed, all the endemic equilibrium points related to the disease are derived, a condition to investigate all possible equilibria of the model in terms of the basic reproduction number is obtained. In last, numerical simulation is presented with and without vaccination or control for the proposed model.
{"title":"The stability analysis and control transmission of mathematical model for Ebola Virus","authors":"M. Tahir, G. Zaman, Syed Inayat Ali Shah, S. Muhammad, S. Hussain, M. Ishaq","doi":"10.30538/psrp-oma2019.0042","DOIUrl":"https://doi.org/10.30538/psrp-oma2019.0042","url":null,"abstract":"Abstract: Mathematical modeling of infectious diseases has progressed dramatically over the past four decades and continues to flourish at the nexus of mathematics, epidemiology, and infectious diseases research. Now recognized as a valuable tool, mathematical models are being integrated into the public health decision-making process more than ever before. In this article, a mathematical model of Ebola virus which is named as SEIVR (susceptible, exposed, infected, vaccinated, recovered) model is considered. First, we formulate the model and present the basic properties of the proposed model. Then, basic reproductive number is obtained by using the next-generation matrix approach. Furthermore, the sensitivity analysis of R0 is also discussed, all the endemic equilibrium points related to the disease are derived, a condition to investigate all possible equilibria of the model in terms of the basic reproduction number is obtained. In last, numerical simulation is presented with and without vaccination or control for the proposed model.","PeriodicalId":52741,"journal":{"name":"Open Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48754028","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 : 2019-12-31DOI: 10.30538/psrp-oma2019.0037
B. Sambo, Gideon Benjamin Meller
{"title":"On certain subclasses of p-valent functions with negative coefficients defined by a generalized differential operator","authors":"B. Sambo, Gideon Benjamin Meller","doi":"10.30538/psrp-oma2019.0037","DOIUrl":"https://doi.org/10.30538/psrp-oma2019.0037","url":null,"abstract":"","PeriodicalId":52741,"journal":{"name":"Open Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46999951","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 : 2019-12-31DOI: 10.30538/psrp-oma2019.0036
Hocine Gabsi, A. Ardjouni, A. Djoudi
Hocine Gabsi1, Abdelouaheb Ardjouni2,∗ and Ahcene Djoudi3 1 Department of Mathematics, University of El-Oued, El-Oued, Algeria.; hocinegabsi@gmail.com 2 Department of Mathematics and Informatics, University of Souk Ahras, P.O. Box 1553, Souk Ahras, 41000, Algeria. 3 Applied Mathematics Lab, Faculty of Sciences, Department of Mathematics, University of Annaba, P.O. Box 12, Annaba 23000, Algeria.; adjoudi@yahoo.com * Correspondence: abd_ardjouni@yahoo.fr
{"title":"Existence of positive periodic solutions of neutral nonlinear differential systems with variable delays","authors":"Hocine Gabsi, A. Ardjouni, A. Djoudi","doi":"10.30538/psrp-oma2019.0036","DOIUrl":"https://doi.org/10.30538/psrp-oma2019.0036","url":null,"abstract":"Hocine Gabsi1, Abdelouaheb Ardjouni2,∗ and Ahcene Djoudi3 1 Department of Mathematics, University of El-Oued, El-Oued, Algeria.; hocinegabsi@gmail.com 2 Department of Mathematics and Informatics, University of Souk Ahras, P.O. Box 1553, Souk Ahras, 41000, Algeria. 3 Applied Mathematics Lab, Faculty of Sciences, Department of Mathematics, University of Annaba, P.O. Box 12, Annaba 23000, Algeria.; adjoudi@yahoo.com * Correspondence: abd_ardjouni@yahoo.fr","PeriodicalId":52741,"journal":{"name":"Open Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42602890","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 : 2019-12-31DOI: 10.30538/psrp-oma2019.0041
D. Ziane, Rachid Belgacem, Ahmed Bokhari
Djelloul Ziane1,2, Rachid Belgacem3,∗ and Ahmed Bokhari3 1 Laboratory of mathematics and its applications (LAMAP), University of Oran1 Ahmed Ben Bella, Oran, 31000, Algeria.; djeloulz@yahoo.com 2 Department of Physics, University of Hassiba Benbouali, Ouled Fares, Chlef 02180, Algeria. 3 Department of Mathematics, University of Hassiba Benbouali, Ouled Fares, Chlef 02180, Algeria.; belgacemrachid02@yahoo.fr (R.B); bokhari.ahmed@ymail.com (A.B) * Correspondence: belgacemrachid02@yahoo.fr
{"title":"A new modified Adomian decomposition method for nonlinear partial differential equations","authors":"D. Ziane, Rachid Belgacem, Ahmed Bokhari","doi":"10.30538/psrp-oma2019.0041","DOIUrl":"https://doi.org/10.30538/psrp-oma2019.0041","url":null,"abstract":"Djelloul Ziane1,2, Rachid Belgacem3,∗ and Ahmed Bokhari3 1 Laboratory of mathematics and its applications (LAMAP), University of Oran1 Ahmed Ben Bella, Oran, 31000, Algeria.; djeloulz@yahoo.com 2 Department of Physics, University of Hassiba Benbouali, Ouled Fares, Chlef 02180, Algeria. 3 Department of Mathematics, University of Hassiba Benbouali, Ouled Fares, Chlef 02180, Algeria.; belgacemrachid02@yahoo.fr (R.B); bokhari.ahmed@ymail.com (A.B) * Correspondence: belgacemrachid02@yahoo.fr","PeriodicalId":52741,"journal":{"name":"Open Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45394772","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 : 2018-12-31DOI: 10.30538/PSRP-OMA2018.0014
Wei Gao, M. Asif, W. Nazeer
Chemical reaction network theory is an area of applied mathematics that attempts to model the behavior of real world chemical systems. Since its foundation in the 1960s, it has attracted a growing research community, mainly due to its applications in biochemistry and theoretical chemistry. It has also attracted interest from pure mathematicians due to the interesting problems that arise from the mathematical structures involved. In this report, we compute newly defined topological indices, namely, Arithmetic-Geometric index (AG1 index), SK index, SK1 index, and SK2 index of the Honey Comb Derived Networks. We also compute sum connectivity index and modified Randić index. Moreover we give geometric comparison of our results. Mathematics Subject Classification: 05C12, 05C90.
{"title":"The Study of Honey Comb Derived Network via Topological Indices","authors":"Wei Gao, M. Asif, W. Nazeer","doi":"10.30538/PSRP-OMA2018.0014","DOIUrl":"https://doi.org/10.30538/PSRP-OMA2018.0014","url":null,"abstract":"Chemical reaction network theory is an area of applied mathematics that attempts to model the behavior of real world chemical systems. Since its foundation in the 1960s, it has attracted a growing research community, mainly due to its applications in biochemistry and theoretical chemistry. It has also attracted interest from pure mathematicians due to the interesting problems that arise from the mathematical structures involved. In this report, we compute newly defined topological indices, namely, Arithmetic-Geometric index (AG1 index), SK index, SK1 index, and SK2 index of the Honey Comb Derived Networks. We also compute sum connectivity index and modified Randić index. Moreover we give geometric comparison of our results. Mathematics Subject Classification: 05C12, 05C90.","PeriodicalId":52741,"journal":{"name":"Open Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49289928","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 : 2018-12-31DOI: 10.30538/psrp-oma2018.0024
K. Atifi, E. Essoufi, Hamed Ould Sidi
This paper deals with the determination of a coefficient in the diffusion term of some degenerate /singular one-dimensional linear parabolic equation from final data observations. The mathematical model leads to a non convex minimization problem. To solve it, we propose a new approach based on a hybrid genetic algorithm (married genetic with descent method type gradient). Firstly, with the aim of showing that the minimization problem and the direct problem are well-posed, we prove that the solution’s behavior changes continuously with respect to the initial conditions. Secondly, we chow that the minimization problem has at least one minimum. Finally, the gradient of the cost function is computed using the adjoint state method. Also we present some numerical experiments to show the performance of this approach. Mathematics Subject Classification: 15A29, 47A52, 93C20, 35K05, 35K65.
{"title":"Identification of a Diffusion Coefficient in Degenerate/Singular Parabolic Equations from Final Observation by Hybrid Method","authors":"K. Atifi, E. Essoufi, Hamed Ould Sidi","doi":"10.30538/psrp-oma2018.0024","DOIUrl":"https://doi.org/10.30538/psrp-oma2018.0024","url":null,"abstract":"This paper deals with the determination of a coefficient in the diffusion term of some degenerate /singular one-dimensional linear parabolic equation from final data observations. The mathematical model leads to a non convex minimization problem. To solve it, we propose a new approach based on a hybrid genetic algorithm (married genetic with descent method type gradient). Firstly, with the aim of showing that the minimization problem and the direct problem are well-posed, we prove that the solution’s behavior changes continuously with respect to the initial conditions. Secondly, we chow that the minimization problem has at least one minimum. Finally, the gradient of the cost function is computed using the adjoint state method. Also we present some numerical experiments to show the performance of this approach. Mathematics Subject Classification: 15A29, 47A52, 93C20, 35K05, 35K65.","PeriodicalId":52741,"journal":{"name":"Open Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44512859","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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