Fractional Langevin Coupled System with Stieltjes Integral Conditions

Rafia Majeed, Binlin Zhang () and Mehboob Alam
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Rafia Majeed: College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China
Binlin Zhang: College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China
Mehboob Alam: Faculty of Engineering Sciences, GIK Institute, Topi 23640, Pakistan

Mathematics, 2023, vol. 11, issue 10, 1-14

Abstract: This article outlines the necessary requirements for a coupled system of fractional order boundary value involving the Caputo fractional derivative, including its existence, uniqueness, and various forms of Ulam stability. We demonstrate the existence and uniqueness of the proposed coupled system by using the cone-type Leray–Schauder result and the Banach contraction principle. Based on the traditional method of nonlinear functional analysis, the stability is examined. An example is used to provide a clear illustration of our main results.

Keywords: caputo derivative; implicit coupled system; existence theory; green function; Ulam stability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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