Winter 2024 A NOTE ON THE EXISTENCE OF SOLUTIONS FOR CAPUTO FRACTIONAL DIFFERENTIAL EQUATIONS
Muhammad N. Islam, Halis Can Koyuncuoğlu, Youssef N. Raffoul
J. Integral Equations Applications 36(4): 437-446 (Winter 2024). DOI: 10.1216/jie.2024.36.437

Abstract

We study the existence of a unique bounded continuous solution of a Caputo fractional differential equation. The results are obtained from an equivalent Volterra integral equation which is derived by inverting the fractional differential equation. The kernel function of this integral equation is weakly singular, and hence the standard techniques that are normally used for Volterra integral equations do not apply here. This hurdle is overcome by using a resolvent equation, applying some known properties of the resolvent, and then employing the contraction mapping principle.

Citation

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Muhammad N. Islam. Halis Can Koyuncuoğlu. Youssef N. Raffoul. "A NOTE ON THE EXISTENCE OF SOLUTIONS FOR CAPUTO FRACTIONAL DIFFERENTIAL EQUATIONS." J. Integral Equations Applications 36 (4) 437 - 446, Winter 2024. https://doi.org/10.1216/jie.2024.36.437

Information

Received: 14 November 2023; Revised: 21 April 2024; Accepted: 13 June 2024; Published: Winter 2024
First available in Project Euclid: 3 October 2024

Digital Object Identifier: 10.1216/jie.2024.36.437

Subjects:
Primary: 34A08 , 45D05 , 45J05

Keywords: Caputo fractional differential equations , contraction mapping , resolvent , unique solution , Volterra integral equations

Rights: Copyright © 2024 Rocky Mountain Mathematics Consortium

Vol.36 • No. 4 • Winter 2024
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