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ISSN:2164-6376 (print)
ISSN:2164-6414 (online)
Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Email: dumitru.baleanu@gmail.com

On Existence and Uniqueness of Solutions to a Class of Fractional Volterra-Fredholm Initial Value Problems

Discontinuity, Nonlinearity, and Complexity 12(4) (2023) 905--916 | DOI:10.5890/DNC.2023.12.014

Abdulrahman A. Sharif$^{1}$, Ahmed A. Hamoud$^2$, Kirtiwant P. Ghadle$^3$

$^{1}$ Department of Mathematics, Hodeidah University, AL-Hudaydah-Yemen

$^{2}$ Department of Mathematics, Taiz University, Taiz-380 015, Yemen

$^{3}$ Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad, India

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Abstract

In this paper, we establish some new conditions for the existence of solutions for a class of nonlinear Caputo fractional Volterra-Fredholm integro-differential equations with initial conditions. The desired results are proved by using Banach fixed point theorem for nonself mappings, fractional inequality and a version of the nonlinear alternative of Leray-Schauder in Banach spaces. Furthermore, the uniqueness results are established by the application of the contraction mapping principle. Finally, some examples are proposed to illustrate our main results.

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