( ω, ρ )-BVP Solution of Impulsive Hadamard Fractional Differential Equations

Ahmad Al-Omari and Hanan Al-Saadi ()
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Ahmad Al-Omari: Department of Mathematics, Faculty of Sciences, Al al-Bayt University, P.O. Box 130095, Mafraq 25113, Jordan
Hanan Al-Saadi: Department of Mathematics, Faculty of Sciences, Umm Al-Qura University, Makkah 24225, Saudi Arabia

Mathematics, 2023, vol. 11, issue 20, 1-18

Abstract: The purpose of this research is to examine the uniqueness and existence of the ( ω , ρ ) -BVP solution for a particular solution to a class of Hadamard fractional differential equations with impulsive boundary value requirements on Banach spaces. The notion of Banach contraction and Schaefer’s theorem are used to prove the study’s key findings. In addition, we offer the prerequisites for the set of solutions to the investigated boundary value with impulsive fractional differential issue to be convex. To enhance the comprehension and practical application of our findings, we offer two illustrative examples at the end of the paper to show how the results can be applied.

Keywords: Hadamard fractional derivative; fixed point; impulsive; mild solution; integro-differential equation; nonlocal condition (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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