A study of fractional differential equations and inclusions involving generalized Caputo-type derivative equipped with generalized fractional integral boundary conditions

Bashir Ahmad; Madeaha Alghanmi; Sotiris K. Ntouyas; Ahmed Alsaedi; Bashir Ahmad; Madeaha Alghanmi; Sotiris K. Ntouyas; Ahmed Alsaedi

doi:10.3934/Math.2019.1.26

AIMS Mathematics

2019, Volume 4, Issue 1: 26-42. doi: 10.3934/Math.2019.1.26

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A study of fractional differential equations and inclusions involving generalized Caputo-type derivative equipped with generalized fractional integral boundary conditions

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, University of Ioannina, 451 10 Ioannina, Greece

Received: 22 October 2018 Accepted: 17 December 2018 Published: 21 December 2018
MSC : 26A33, 34A60, 34B15

In this paper, we introduce a new kind of generalized fractional integral boundary conditions and develop the existence theory for a fractional di erential equation involving generalized Caputotype fractional derivative equipped with these conditions. We also study the inclusion case of the given problem. Examples are constructed to demonstrate the application of the obtained results.
- differential equations and inclusion,
- generalized Caputo derivative,
- fractional integral,
- existence,
- fixed point
Citation: Bashir Ahmad, Madeaha Alghanmi, Sotiris K. Ntouyas, Ahmed Alsaedi. A study of fractional differential equations and inclusions involving generalized Caputo-type derivative equipped with generalized fractional integral boundary conditions[J]. AIMS Mathematics, 2019, 4(1): 26-42. doi: 10.3934/Math.2019.1.26

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Abstract

In this paper, we introduce a new kind of generalized fractional integral boundary conditions and develop the existence theory for a fractional di erential equation involving generalized Caputotype fractional derivative equipped with these conditions. We also study the inclusion case of the given problem. Examples are constructed to demonstrate the application of the obtained results.

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