ON A COUPLED INTEGRO-DIFFERENTIAL SYSTEM INVOLVING MIXED FRACTIONAL DERIVATIVES AND INTEGRALS OF DIFFERENT ORDERS

doi:10.1007/s10473-021-0420-x

数学物理学报(英文版) ›› 2021, Vol. 41 ›› Issue (4): 1366-1384.doi: 10.1007/s10473-021-0420-x

ON A COUPLED INTEGRO-DIFFERENTIAL SYSTEM INVOLVING MIXED FRACTIONAL DERIVATIVES AND INTEGRALS OF DIFFERENT ORDERS

Bashir AHMAD¹, Ravi P. AGARWAL², Abrar BROOM³, Ahmed ALSAEDI³

1. Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia;
2. Department of Mathematics, Texas A & M University, Kingsville, Texas 78363-8202, USA;
3. Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia

收稿日期:2020-03-26 修回日期:2020-07-04 出版日期:2021-08-25 发布日期:2021-09-01
作者简介:Bashir AHMAD,E-mail:bashirahmad qau@yahoo.com;Ravi P. AGARWAL,E-mail:Ravi.Agarwal@tamuk.edu;Abrar BROOM,E-mail:abrarbroom1992@gmail.com; Ahmed ALSAEDI,E-mail:aalsaedi@hotmail.com
基金资助:
This project was funded by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah, Saudi Arabia (KEP-MSc-63-130-42).

ON A COUPLED INTEGRO-DIFFERENTIAL SYSTEM INVOLVING MIXED FRACTIONAL DERIVATIVES AND INTEGRALS OF DIFFERENT ORDERS

Bashir AHMAD¹, Ravi P. AGARWAL², Abrar BROOM³, Ahmed ALSAEDI³

1. Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia;
2. Department of Mathematics, Texas A & M University, Kingsville, Texas 78363-8202, USA;
3. Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia

Received:2020-03-26 Revised:2020-07-04 Online:2021-08-25 Published:2021-09-01
Supported by:
This project was funded by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah, Saudi Arabia (KEP-MSc-63-130-42).

摘要/Abstract

摘要： By applying the standard fixed point theorems, we prove the existence and uniqueness results for a system of coupled differential equations involving both left Caputo and right Riemann-Liouville fractional derivatives and mixed fractional integrals, supplemented with nonlocal coupled fractional integral boundary conditions. An example is also constructed for the illustration of the obtained results.

关键词: Fractional differential equations, Caputo and Riemann-Liouville fractional derivatives, systems, existence, fixed point theorems

Abstract: By applying the standard fixed point theorems, we prove the existence and uniqueness results for a system of coupled differential equations involving both left Caputo and right Riemann-Liouville fractional derivatives and mixed fractional integrals, supplemented with nonlocal coupled fractional integral boundary conditions. An example is also constructed for the illustration of the obtained results.

Key words: Fractional differential equations, Caputo and Riemann-Liouville fractional derivatives, systems, existence, fixed point theorems

中图分类号:

34A08

Bashir AHMAD, Ravi P. AGARWAL, Abrar BROOM, Ahmed ALSAEDI. ON A COUPLED INTEGRO-DIFFERENTIAL SYSTEM INVOLVING MIXED FRACTIONAL DERIVATIVES AND INTEGRALS OF DIFFERENT ORDERS[J]. 数学物理学报(英文版), 2021, 41(4): 1366-1384.

Bashir AHMAD, Ravi P. AGARWAL, Abrar BROOM, Ahmed ALSAEDI. ON A COUPLED INTEGRO-DIFFERENTIAL SYSTEM INVOLVING MIXED FRACTIONAL DERIVATIVES AND INTEGRALS OF DIFFERENT ORDERS[J]. Acta mathematica scientia,Series B, 2021, 41(4): 1366-1384.

参考文献

[1] Ntouyas S K, Broom A, Alsaedi A, et al. Existence results for a nonlocal coupled system of differential equations involving mixed right and left fractional derivatives and integrals. Symmetry, 2020, 12:578
[2] Kilbas A A, Srivastava H M, Trujillo J J. Theory and applications of fractional differential equations. Amsterdam:North-Holland Mathematics Studies, 204. Elsevier Science BV, 2006
[3] Sabatier J, Agrawal O P, Machado J A T. Advances in fractional calculus:theoretical developments and applications in physics and engineering. Dordrecht:Springer, 2007
[4] Ahmad B, Alsaedi A, Ntouyas S K, et al. Hadamard-type fractional differential equations, inclusions and inequalities. Cham:Springer, 2017
[5] Peng L, Zhou Y. Bifurcation from interval and positive solutions of the three-point boundary value problem for fractional differential equations. Appl Math Comput, 2015, 257:458-466
[6] Cui Y, Ma W, Sun Q, et al. New uniqueness results for boundary value problem of fractional differential equation. Nonlinear Anal Model Control, 2018, 23:31-39
[7] Baghani H, Nieto J J. On fractional Langevin equation involving two fractional orders in different intervals. Nonlinear Anal Model Control, 2019, 24:884-897
[8] Alsaedi A, Ahmad B, Alghanmi M. Extremal solutions for generalized Caputo fractional differential equations with Steiltjes-type fractional integro-initial conditions. Appl Math Lett, 2019, 91:113120
[9] Ahmad B, Alsaedi A, Alruwaily Y, et al. Nonlinear multi-term fractional differential equations with Riemann-Stieltjes integro-multipoint boundary conditions. AIMS Math, 2020, 5:1446-1461
[10] Liang S, Wang L, Yin G. Fractional differential equation approach for convex optimization with convergence rate analysis. Optim Lett, 2020, 14:145-155
[11] Iskenderoglu G, Kaya D. Symmetry analysis of initial and boundary value problems for fractional differential equations in Caputo sense. Chaos Solitons Fractals, 2020, 134:109684
[12] Cen Z, Liu L B, Huang J. A posteriori error estimation in maximum norm for a two-point boundary value problem with a Riemann-Liouville fractional derivative. Appl Math Lett, 2020, 102:106086, 8 pp
[13] Javidi M, Ahmad B. Dynamic analysis of time fractional order phytoplankton-toxic phytoplanktonzooplankton system. Ecological Modelling, 2015, 318:8-18
[14] Carvalho A, Pinto C M A. A delay fractional order model for the co-infection of malaria and HIV/AIDS. Int J Dyn Control, 2017, 5:168-186
[15] Zhang F, Chen G, Li C, et al. Chaos synchronization in fractional differential systems. Phil Trans R Soc A, 2013, 371:20120155
[16] Henderson J, Luca R, Tudorache A. On a system of fractional differential equations with coupled integral boundary conditions. Fract Calc Appl Anal, 2015, 18:361-386
[17] Ahmad B, Luca R. Existence of solutions for a system of fractional differential equations with coupled nonlocal boundary conditions. Fract Calc Appl Anal, 2018, 21:423-441
[18] Alsaedi A, Ahmad B, Aljoudi S, et al. A study of a fully coupled two-parameter system of sequential fractional integro-differential equations with nonlocal integro-multipoint boundary conditions. Acta Mathematica Scientia, 2019, 39B:927-944
[19] Ntouyas S K, Al-Sulami H H. A study of coupled systems of mixed order fractional differential equations and inclusions with coupled integral fractional boundary conditions. Adv Difference Equ, 2020, 73
[20] Atanackovic T M, Stankovic B. On a differential equation with left and right fractional derivatives. Fract Calc Appl Anal, 2007, 10:139-150
[21] Zimbardo G, Perri S. On the Fractional Diffusion-Advection Equation for Fluids and Plasmas. Fluids, 2019, 4:62
[22] Khaldi R, Guezane-Lakoud A. Higher order fractional boundary value problems for mixed type derivatives. J Nonlinear Funct Anal, 2017, 30:1-9
[23] Lakoud A G, Khaldi R, Kilicman A. Existence of solutions for a mixed fractional boundary value problem. Adv Differ Equ, 2017, 164
[24] Guezane-Lakoud A, Khaldi R, Torres D F M. On a fractional oscillator equation with natural boundary conditions. Progr Fract Differ Appl, 2017, 3:191-197
[25] Ahmad B, Ntouyas S K, Alsaedi A. Existence theory for nonlocal boundary value problems involving mixed fractional derivatives. Nonlinear Anal Model Control, 2019, 24:937-957
[26] Smart D R. Fixed point theorems. London:Cambridge University Press, 1974

ON A COUPLED INTEGRO-DIFFERENTIAL SYSTEM INVOLVING MIXED FRACTIONAL DERIVATIVES AND INTEGRALS OF DIFFERENT ORDERS

ON A COUPLED INTEGRO-DIFFERENTIAL SYSTEM INVOLVING MIXED FRACTIONAL DERIVATIVES AND INTEGRALS OF DIFFERENT ORDERS

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