EXISTENCE OF SOLUTIONS FOR 2D NONLINEAR FRACTIONAL VOLTERRA INTEGRAL EQUATIONS IN BANACH SPACE

Parul Saini; Ümit Çakan; Amar Deep

doi:10.1216/rmj.2023.53.1965

Abstract

We study the existence of solutions for 2D fractional Volterra integral equations, using Petryshyn’s fixed-point theorem and measures of noncompactness in the Banach space $C(\lbrack0,a\rbrack\times\lbrack0,b\rbrack,\mathbb{R})$ . Our results generalize results gained from earlier studies under some weaker conditions. We present some examples applying our results.

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Parul Saini. Ümit Çakan. Amar Deep. "EXISTENCE OF SOLUTIONS FOR 2D NONLINEAR FRACTIONAL VOLTERRA INTEGRAL EQUATIONS IN BANACH SPACE." Rocky Mountain J. Math. 53 (6) 1965 - 1981, December 2023. https://doi.org/10.1216/rmj.2023.53.1965

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Received: 14 September 2022; Revised: 7 October 2022; Accepted: 11 October 2022; Published: December 2023

First available in Project Euclid: 21 December 2023

MathSciNet: MR4682753

zbMATH: 07784585

Digital Object Identifier: 10.1216/rmj.2023.53.1965

Subjects:

Primary: 47H09 , 47H10

Secondary: 45D05

Keywords: fixed-point theorem , fractional integral equation , measure of noncompactness

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