On integrable and approximate solutions for Hadamard fractional quadratic integral equations-Reference-Cited by-同舟云学术

On integrable and approximate solutions for Hadamard fractional quadratic integral equations

Published:2024 Issue:3 Volume:9 Page:5746-5762
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Aldosary Saud Fahad¹,Metwali Mohamed M. A.²,Kazemi Manochehr³,Alsaadi Ateq⁴

Affiliation:

1. Department of Mathematics, College of Science and Humanities in Alkharj, Prince Sattam bin Abdulaziz University, Alkharj 11942, Saudi Arabia

2. Department of Mathematics and Computer Science, Faculty of Science, Damanhour University, Damanhour, Egypt

3. Department of Mathematics, Ashtian Branch, Islamic Azad University, Ashtian, Iran

4. Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia

Abstract

<abstract><p>This article addressed the integrable and approximate solutions of Hadamard-type fractional Gripenberg's equation in Lebesgue spaces $ L_1[1, e] $. It is well known that the Gripenberg's equation has significant applications in mathematical biology. By utilizing the fixed point (FPT) approach and the measure of noncompactness (MNC), we demonstrated the presence of monotonic integrable solutions as well as the uniqueness of the solution for the studied equation in spaces that are not Banach algebras. Moreover, the method of successive approximations was successfully applied and, as a result, we obtained the approximate solutions for these integral equations. To validate the obtained results, we provided several numerical examples.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

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