Novel results on positive solutions for nonlinear Caputo–Hadamard fractional Volterra–Fredholm integro differential equations

Abdulrahman A. Sharif^a, Maha M. Hamood^b, Kirtiwant P. Ghadle<sup>c

a</sup> Department of Mathematics, Hodeidah University, AL-Hudaydah, Yemen
^b Department of Mathematics, Taiz University, Taiz, Yemen
^c Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad-431 004 (M.S.), India

Abstract: In this paper, we establish the existence and uniqueness of positive solutions for fractional Volterra–Fredholm integro-differential equation. This equation incorporates Caputo–Hadamard fractional derivatives and is defined with initial conditions. Our proof methodology relies on the Schauder fixed point theorem, the Banach contraction principle, upper and lower solution concepts, and their applications. To illustrate the significance of our theoretical findings, we also present a compelling example.

Keywords: fractional Volterra–Fredholm integro-differential equation, positive solutions, fixed point method.

UDC: 519

Received: 10.08.2024
Received in revised form: 15.09.2024
Accepted: 24.10.2024

Language: English