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Open AccessArticle

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

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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
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Department of Mathematics, Texas A&M University, Kingsville, TX 78363-8202, USA
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Author to whom correspondence should be addressed.
Mathematics 2019, 7(11), 1108; https://doi.org/10.3390/math7111108
Received: 1 October 2019 / Revised: 6 November 2019 / Accepted: 11 November 2019 / Published: 15 November 2019
(This article belongs to the Special Issue Mathematical Analysis and Boundary Value Problems)
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. View Full-Text
Keywords: multi-orders fractional derivatives; impulse; caputo-type generalized fractional derivative; delay; fractional integral; existence; fixed point multi-orders fractional derivatives; impulse; caputo-type generalized fractional derivative; delay; fractional integral; existence; fixed point
MDPI and ACS Style

Ahmad, B.; Alghanmi, M.; Alsaedi, A.; Agarwal, R.P. Nonlinear Impulsive Multi-Order Caputo-Type Generalized Fractional Differential Equations with Infinite Delay. Mathematics 2019, 7, 1108.

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