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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

Existence, Uniqueness and Stability Results of Fractional Volterra-Fredholm Integro Differential Equations of $psi$-Hilfer Type

Discontinuity, Nonlinearity, and Complexity 10(3) (2021) 535--545 | DOI:10.5890/DNC.2021.09.013

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

$^{1}$ Department of Mathematics, Taiz University, Taiz-380 015, Yemen

$^{2}$ 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 and uniqueness of solutions for a class of nonlinear $\psi$-Hilfer fractional Volterra-Fredholm integro differential equations with boundary conditions. In addition, the Ulam-Hyers stability for solutions of the given problem are also discussed. The desired results are proved by using generalized Gronwall inequality, aid of fixed point theorems due to Banach and Schauder in weighted spaces.

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