NONLINEAR LANGEVIN FRACTIONAL DIFFERENTIAL EQUATION WITH NONLOCAL MIXED BOUNDARY CONDITIONS INVOLVING A CAPUTO-EXPONENTIAL

In this paper, the existence and uniqueness results for a nonlinear Langevin fractional differential equation with nonlocal mixed (multipoint, fractional integral and fractional derivative) boundary conditions involving a Caputo-exponential is studied. The uniqueness result is discussed via Banach&#...

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Bibliographic Details
Published inTWMS journal of applied and engineering mathematics Vol. 15; no. 8; p. 1901
Main Author Derdar, N
Format Journal Article
LanguageEnglish
Published Turkic World Mathematical Society 01.08.2025
Subjects
Differential equations
Langevin, Paul
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Summary:In this paper, the existence and uniqueness results for a nonlinear Langevin fractional differential equation with nonlocal mixed (multipoint, fractional integral and fractional derivative) boundary conditions involving a Caputo-exponential is studied. The uniqueness result is discussed via Banach's contraction mapping principle, and the existence of solutions is proved by using Schaefer's fixed point theorem. Finally, an example is also constructed to demonstrate the application of the main results. Keywords: Langevin equation, Caputo's-exponential fractional derivative, implicit fractional differential, nonlocal mixed boundary conditions, fixed point theorems. AMS Subject Classification: 35B40, 35L70.
ISSN:2146-1147