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TWO-VARIABLE JACOBI POLYNOMIALS FOR SOLVING SOME FR ACTIONAL PA RTIAL DIFFERENTIAL EQUATIONS

Journal of Computational Mathematics 2020年第6期38卷 879-902页

作者： Jafar Biazar khadijeh sadri Department of Applied Mathematics Faculty of Mathematical SciencesUniversity of GuilanP.O.Box 41335-1914GuilanRashtIran

Tw o variable Jacobi polynomials,as a two-dimensional basis,are applied to solve a class of temporal fractional partial differential *** fractional derivative operators are in the Caputo *** operational matrices of the integration of integer and fractional orders are *** these matrices together with the Tau Jacobi method converts the main problem into the corresponding system of algebraic *** error bound is obtained in a two-dimensional Jacobi-weighted Sobolev ***,the efficiency of the proposed method is demonstrated by implementing the algorithm to several illustrative *** will be compared witli those obtained from some existing methods.

关键词： Fractional partial differential equation Two-variable Jacobi polynomials Caputo derivative Error bound.

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Optimal control of combined antiretroviral therapies in an HIV infection model with cure rate and fusion effect

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International Journal of Biomathematics 2023年第1期16卷 29-51页

作者： Bhagya Jyoti Nath Kaushik Dehingia khadijeh sadri Hemanta Kumar Sarmah Kamyar Hosseini Choonkil Park Department of Mathematics Barnagar College Sorbhog 781317BarpetaAssamIndia Department of Mathematics Sonari College Sonari 785690CharaideoAssamIndia Department of Mathematics Rasht Branch Islamic Azad UniversityRashtIran Department of Mathematics Gauhati University Guwahati781014AssamIndia Department of Mathematics Near East University TRNC Mersin10Turkey Research Institute for Natural Sciences Hanyang University Seoul 04763South Korea

This paper mainly targets to deduce an optimal treatment strategy for combined antiretroviral drugs,which can maximize healthy CD4^(+)T cells level with minimum side effects and *** this purpose,we consider a within-host treatment model for the HIV infection with two controls incorporating full logistic proliferation of healthy CD4^(+)T cells,cure rate and fusion *** two controls represent the effects of reverse transcriptase inhibitors(RTIs)and protease inhibitors(PIs),*** model analysis begins with proving different basic properties like non-negativity,boundedness of the model solutions and calculation of the basic reproduction number of the model under ***,stability results are obtained for HIV infection-free equilibrium point and also,a critical efficacy for the combined therapies is *** that,the optimal control problem is proposed and solved numerically using a forwardbackward iterative ***,we obtain an optimal treatment strategy that can maximize healthy CD4^(+)T cells count and control the viral load,and HIV-infected CD4^(+)T cells count to an undetectable level resulting in improved health conditions of infected individuals.

关键词： HIV infection antiretroviral drugs critical efficacy optimal control Pontryagin's maximum principle.

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