Existence and uniqueness theorems for nonlinear coupled boundary value problem of the \(\mathcal{ABC}\) fractional differential equation

Volume 37, Issue 3, pp 297--318 https://dx.doi.org/10.22436/jmcs.037.03.04

Publication Date: October 04, 2024 Submission Date: July 01, 2024 Revision Date: July 26, 2024 Accteptance Date: September 03, 2024

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Authors

G. Janardhanan - Department of Mathematics‎, ‎Saveetha School of Engineering‎, ‎Saveetha Institute of Medical and Technical Sciences, Saveetha University, Chennai 602 105‎, Tamil Nadu, India. G. Mani - Department of Mathematics‎, ‎Saveetha School of Engineering‎, ‎Saveetha Institute of Medical and Technical Sciences, Saveetha University, Chennai 602 105‎, Tamil Nadu, India. D. Santina - Department of Mathematics and Sciences, ‎Prince Sultan University, ‎Riyadh 11586, ‎Saudi Arabia. N. Mlaiki - Department of Mathematics and Sciences, ‎Prince Sultan University, ‎Riyadh 11586, ‎Saudi Arabia.

Abstract

‎In this paper‎, ‎we study existence and uniqueness of solutions for a new systems of nonlinear coupled boundary value problem of the \(\mathcal{ABC}\) fractional differential equation‎. ‎By applying the Banach's‎ ‎fixed point theorem and Krasnoselskii's fixed point theorem‎, ‎the existence of solutions is obtained‎. ‎Further‎, ‎the provided problem Ulam-Hyers (\(\mathcal{UH}\)) and generalized Ulam-Hyers (\(\mathcal{GUH}\)) stability are both investigated‎. ‎The result obtained in this work are well illustrated with the aid of examples‎.

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Keywords

• \(\mathcal{ABC}\) fractional differential equation
• boundary value problem
• existence and uniqueness
• ‎\(\mathcal{UH}\) stability
• generalized \(\mathcal{UH}\) stability
• fixed point theorem

MSC

•  34A08‎
•  ‎34A12
•  47H10

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