Forward and Inverse Problems for a Langevin-Type Fractional Equation Involving Non-Local Time Condition

2025/07/10 by F Yusuf, Yusuf, Fayziev, Jumaeva Shakhnoza +1
Mathematics · #34A12 #35R11 #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Fractional Differential Equations Solutions #Nonlinear Differential Equations Analysis

paper · pdf · doi:10.48550/arxiv.2507.07446

openalex publication_date 2025/07/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The paper addresses the formulation and analysis of direct and inverse problems for a Langevin-type fractional differential equation under a non-local condition imposed on the time variable. An additional condition for solving the inverse problem has the form u(t₀)=ω. The existence and uniqueness of a solution to the problems are established, and stability inequalities are derived. Criteria ensuring the uniqueness of the solution are identified.

Citations

• On the Cauchy problem for the Langevin-type fractional equation
• Langevin Approach to Fractional Diffusion Equations including Inertial Effects

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