Analytic Solutions for Hilfer Type Fractional Langevin Equations with Variable Coefficients in a Weighted Space-Reference-Cited by-同舟云学术

Analytic Solutions for Hilfer Type Fractional Langevin Equations with Variable Coefficients in a Weighted Space

Published:2024-04-23 Issue:5 Volume:13 Page:284
ISSN:2075-1680
Container-title:Axioms
language:en
Short-container-title:Axioms

Author:

Li Fang¹^ORCID,Yang Ling¹,Wang Huiwen¹

Affiliation:

1. School of Mathematics, Yunnan Normal University, Kunming 650500, China

Abstract

In this work, analytic solutions of initial value problems for fractional Langevin equations involving Hilfer fractional derivatives and variable coefficients are studied. Firstly, the equivalence of an initial value problem to an integral equation is proved. Secondly, the existence and uniqueness of solutions for the above initial value problem are obtained without a contractive assumption. Finally, a formula of explicit solutions for the proposed problem is derived. By using similar arguments, corresponding conclusions for the case involving Riemann–Liouville fractional derivatives and variable coefficients are obtained. Moreover, the nonlinear case is discussed. Two examples are provided to illustrate theoretical results.

Funder

Natural Science Foundation of China

Publisher

MDPI AG

Link

https://www.mdpi.com/2075-1680/13/5/284/pdf

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