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