Analysis of Neutral Implicit Stochastic Hilfer Fractional Differential Equation Involving Lévy Noise with Retarded and Advanced Arguments

Hamza Khalil, Akbar Zada (), Mohamed Rhaima and Ioan-Lucian Popa
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Hamza Khalil: Department of Mathematics, University of Peshawar, Peshawar 25120, Pakistan
Akbar Zada: Department of Mathematics, University of Peshawar, Peshawar 25120, Pakistan
Mohamed Rhaima: Department of Statistics and Operations Research, College of Sciences, King Saud University, Riyadh 11451, Saudi Arabia
Ioan-Lucian Popa: Department of Computing, Mathematics and Electronics, “1 Decembrie 1918” University of Alba Iulia, 510009 Alba Iulia, Romania

Mathematics, 2024, vol. 12, issue 21, 1-15

Abstract: This paper investigates the qualitative properties of the solutions for neutral implicit stochastic Hilfer fractional differential equations involving Lévy noise with retarded and advanced arguments. The existence property of the solution of the aforementioned equation is demonstrated by the Mónch condition, and the uniqueness is demonstrated by the remarkable fixed point of Banach. In addition, we examine the Hyers–Ulam ( HU ) stability of the presented mathematical models. To substantiate our theoretical conclusions, a real-world example is included to illustrate their practical application.

Keywords: Hilfer fractional derivative; stochastic; Lévy noise; existence; Ulam stability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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