On boundary values system of sequential hybrid fractional differential equations

Volume 34, Issue 3, pp 268--282 https://dx.doi.org/10.22436/jmcs.034.03.06

Publication Date: March 29, 2024 Submission Date: October 22, 2023 Revision Date: December 11, 2023 Accteptance Date: February 16, 2024

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Authors

K. Shah - Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia. - Department of Mathematics, University of Malakand, Chakdara, Dir(L),18000, KPK, Pakistan. Sh. Gul - Department of Mathematics, University of Malakand, Chakdara, Dir(L),18000, KPK, Pakistan. R. A. Khan - Department of Mathematics, University of Malakand, Chakdara, Dir(L),18000, KPK, Pakistan. Th. Abdeljawad - Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia.

Abstract

This work is devoted to study a broad system of sequential hybrid fractional differential equations (S-HFDEs). Sufficient conditions related to the existence theory for the aforementioned system are investigated by utilizing the coincidence degree theory of topology. The mentioned degree theory is a powerful instrument which can be utilized to examine a wide range of nonlinear problems for qualitative theory. In addition, for the system of boundary value problems (BVPs) of S-HFDEs under consideration, a result concerning the Ullam-Hyers (U-H) stability is also developed. A pertinent example is also given to verify our theoretical results.

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Keywords

• Caputo derivative
• degree theory
• nonlinear analysis

MSC

•  26A33
•  34A08
•  35A09

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