J. Nonl. Evol. Equ. Appl. 2021 (3), pp. 41-62, published on April 21, 2021:

On existence and uniqueness of integral solutions for a class of nondensely defined mixed Volterra-Fredholm integro-fractional neutral differential equations

B. Roy, S. N. Bora

Department of Mathematics, Indian Institute of Technology Guwahati, Guwahati 781039, India

Received on July 31, 2020, revised version on January 10, 2021
Accepted on January 19, 2021

Communicated by Mouffak Benchohra

Abstract.  In this article, a class of fractional integro-differential equations of mixed type is considered and some sufficient conditions in connection with the existence of integral solutions are established with the help of the fixed point theorems due to Banach, Krasnoselskii and Darbo-Sadovskii,and also the fixed point theorem for condensing maps. Two of the results are verified by considering appropriate examples.
Keywords:Volterra-Fredholm integro-differential equation, Hille-Yosida condition, integral solution, fixed-point theorem, measure of noncompactness.
2010 Mathematics Subject Classification:   26A33, 34G20, 47H10, 47H08.

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