q -Fractional Langevin Differential Equation with q -Fractional Integral Conditions

Wuyang Wang, Khansa Hina Khalid, Akbar Zada (), Sana Ben Moussa and Jun Ye
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Wuyang Wang: Bell Honors School, Nanjing University of Posts and Telecommunications, Nanjing 210023, China
Khansa Hina Khalid: Department of Mathematics, University of Peshawar, Peshawar 25120, Pakistan
Akbar Zada: Department of Mathematics, University of Peshawar, Peshawar 25120, Pakistan
Sana Ben Moussa: Faculty of Science and Arts, Mohail Asser, King Khalid University, Abha 61421, Saudi Arabia
Jun Ye: College of Science, Nanjing University of Posts and Telecommunications, Nanjing 210023, China

Mathematics, 2023, vol. 11, issue 9, 1-27

Abstract: The major goal of this manuscript is to investigate the existence, uniqueness, and stability of a q -fractional Langevin differential equation with q -fractional integral conditions. We demonstrate the existence and uniqueness of the solution to the proposed q -fractional Langevin differential equation using the Banach contraction principle and Schaefer’s fixed-point theorem. We also elaborate on different kinds of Ulam stability. The theoretical outcomes are verified by examples.

Keywords: Langevin equations; fractional q -differential equation; Caputo derivative; 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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