SOME RESULTS OF EXISTENCE AND CONTINUOUS DEPENDENCE ON ψ- HILFER FRACTIONAL INTEGRODIFFRENTIAL EQUATIONS
By
Seema S. Ubale and Deepak B. Pachpatte
Department of mathematics, Dr. Babasaheb Ambedkar Marathwada University, Chh. Sambhajinagar Maharashtra, India-431004
Email: seemasahebraoubale@gmail.com, pachpatte@gmail.com
(Received: August 26, 2023; In format: March 23, 2025; Revised: April 22, 2025; Accepted: April 25, 2025)
DOI: https://doi.org/10.58250/jnanabha.2025.55107
Abstract
In this paper, we study the existence and uniqueness results of the solutions for nonlinear fractional Volterra integral and integrodifferential equations involving ψ-Hilfer fractional derivative. The tools used in the analysis are fractional-order integral inequalities and an adequate norm k.kη,∞ in Banach space. Besides, we study their continuous dependence.
2020 Mathematical Sciences Classification: 26A33;26D10;26D15
Keywords and Phrases: Fractional integrodifferential equation, ψ-Hilfer fractional derivative, Existence, Uniqueness