<i>q</i>-Fractional Langevin Differential Equation with <i>q</i>-Fractional Integral Conditions

<i>q</i>-Fractional Langevin Differential Equation with <i>q</i>-Fractional Integral Conditions

The major goal of this manuscript is to investigate the existence, uniqueness, and stability of a <i>q</i>-fractional Langevin differential equation with <i>q</i>-fractional integral conditions. We demonstrate the existence and uniqueness of the solution to the proposed <i...

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Bibliographic Details
Main Authors: Wuyang Wang, Khansa Hina Khalid, Akbar Zada, Sana Ben Moussa, Jun Ye
Format: Article
Language:English
Published: MDPI AG 2023-05-01
Series:Mathematics
Subjects:
Langevin equations
fractional <i>q</i>-differential equation
Caputo derivative
green function
Ulam stability
Online Access:https://www.mdpi.com/2227-7390/11/9/2132
Description
Summary:The major goal of this manuscript is to investigate the existence, uniqueness, and stability of a <i>q</i>-fractional Langevin differential equation with <i>q</i>-fractional integral conditions. We demonstrate the existence and uniqueness of the solution to the proposed <i>q</i>-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.
ISSN:2227-7390

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