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

Bashir AHMAD; Ravi P. AGARWAL; Abrar BROOM; Ahmed ALSAEDI

doi:10.1007/s10473-021-0420-x

Acta mathematica scientia, Series B >

2021 , Vol. 41 >Issue 4: 1366 - 1384

DOI: https://doi.org/10.1007/s10473-021-0420-x

Articles

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

Bashir AHMAD ,
Ravi P. AGARWAL ,
Abrar BROOM ,
Ahmed ALSAEDI

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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 date: 2020-03-26

Revised date: 2020-07-04

Online 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).

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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

Cite this article

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 . DOI: 10.1007/s10473-021-0420-x

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