August 2023 UNIQUENESS OF SOLUTIONS, STABILITY AND SIMULATIONS FOR A DIFFERENTIAL PROBLEM INVOLVING CONVERGENT SERIES AND TIME VARIABLE SINGULARITIES
Yazid Gouari, Zoubir Dahmani, Meriem Mansouria Belhamiti, Mehmet Zeki Sarikaya
Rocky Mountain J. Math. 53(4): 1099-1116 (August 2023). DOI: 10.1216/rmj.2023.53.1099

Abstract

We study a new problem of nonlinear integrodifferential equations with nonlocal integral conditions. The considered problem is singular at the origin of the time axis and it involves convergent series combined with Riemann–Liouville integrals. We prove an existence and uniqueness result for our problem. Some examples are given to illustrate the uniqueness result. The Ulam–Hyers stability for the problem is also studied. Then, thanks to some numerical techniques, that allow us to approximate the Caputo derivatives, and by using the Runge–Kutta method, we present a numerical study with some simulations to show more comprehension of the proposed examples.

Citation

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Yazid Gouari. Zoubir Dahmani. Meriem Mansouria Belhamiti. Mehmet Zeki Sarikaya. "UNIQUENESS OF SOLUTIONS, STABILITY AND SIMULATIONS FOR A DIFFERENTIAL PROBLEM INVOLVING CONVERGENT SERIES AND TIME VARIABLE SINGULARITIES." Rocky Mountain J. Math. 53 (4) 1099 - 1116, August 2023. https://doi.org/10.1216/rmj.2023.53.1099

Information

Received: 30 May 2022; Revised: 17 August 2022; Accepted: 18 August 2022; Published: August 2023
First available in Project Euclid: 30 August 2023

MathSciNet: MR4634992
Digital Object Identifier: 10.1216/rmj.2023.53.1099

Subjects:
Primary: 30C45 , 39B72 , 39B82

Keywords: Caputo derivative , fixed point , Runge–Kutta method , singular differential equation , Ulam–Hyers stability

Rights: Copyright © 2023 Rocky Mountain Mathematics Consortium

Vol.53 • No. 4 • August 2023
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