CAPUTO-TYPE FRACTIONAL SYSTEMS WITH VARIABLE ORDER DEPENDING ON THE IMPULSES AND CHANGING THE KERNEL

Thabet Abdeljawad, Nabil Mlaiki and Mohammed S. Abdo
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Thabet Abdeljawad: Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia†Department of Medical Research, China Medical University, Taichung 40402, Taiwan
Nabil Mlaiki: Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia
Mohammed S. Abdo: ��Department of Mathematics, Hodeidah University, P. O. Box 3114, Al-Hudaydah, Yemen

FRACTALS (fractals), 2022, vol. 30, issue 08, 1-15

Abstract: In this paper, we introduce a new class of fractional impulsive systems of functions with respect to another function in which the order of the fractional derivative and the kernel function is associated with the impulses. We derive the solution representation, investigate the existence, and uniqueness of solutions of such a Caputo-type fractional impulsive system. Besides, the data dependence of the system is discussed. Our arguments are based on some classical fixed-point styles. Three various examples are provided to illustrate the validation of the main results. An open problem is presented in the conclusion section to bring the attention to a more general setting.

Keywords: Caputo Impulsive Systems; Existence Theory; Fixed-Point Theorem (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22402198

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