Three-Point Boundary Value Problems for the Langevin Equation with the Hilfer Fractional Derivative

Athasit Wongcharoen, Bashir Ahmad, Sotiris K. Ntouyas and Jessada Tariboon

Advances in Mathematical Physics, 2020, vol. 2020, 1-11

Abstract:

We discuss the existence and uniqueness of solutions for the Langevin fractional differential equation and its inclusion counterpart involving the Hilfer fractional derivatives, supplemented with three-point boundary conditions by means of standard tools of the fixed-point theorems for single and multivalued functions. We make use of Banach’s fixed-point theorem to obtain the uniqueness result, while the nonlinear alternative of the Leray-Schauder type and Krasnoselskii’s fixed-point theorem are applied to obtain the existence results for the single-valued problem. Existence results for the convex and nonconvex valued cases of the inclusion problem are derived via the nonlinear alternative for Kakutani’s maps and Covitz and Nadler’s fixed-point theorem respectively. Examples illustrating the obtained results are also constructed. (2010) Mathematics Subject Classifications . This study is classified under the following classification codes: 26A33; 34A08; 34A60; and 34B15.

Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlamp:9606428

DOI: 10.1155/2020/9606428

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