Nonlinear Impulsive Multi-Order Caputo-Type Generalized Fractional Differential Equations with Infinite Delay

Bashir Ahmad, Madeaha Alghanmi, Ahmed Alsaedi and Ravi P. Agarwal
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Bashir Ahmad: 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
Madeaha Alghanmi: 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
Ahmed Alsaedi: 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
Ravi P. Agarwal: 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

Mathematics, 2019, vol. 7, issue 11, 1-15

Abstract: We establish sufficient conditions for the existence of solutions for a nonlinear impulsive multi-order Caputo-type generalized fractional differential equation with infinite delay and nonlocal generalized integro-initial value conditions. The existence result is proved by means of Krasnoselskii’s fixed point theorem, while the contraction mapping principle is employed to obtain the uniqueness of solutions for the problem at hand. The paper concludes with illustrative examples.

Keywords: multi-orders fractional derivatives; impulse; caputo-type generalized fractional derivative; delay; fractional integral; existence; fixed point (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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