Inverse Kernel Identification in a Time‐Fractional Integro‐Differential Equation

ABSTRACT This article investigates a fractional diffusion‐wave model incorporating memory effects. We first analyze the direct problem and establish the existence, uniqueness, and regularity of its solution under suitable conditions. The primary focus is on an inverse problem, in which an unknown time‐dependent kernel is determined using additional information about the solution. We reformulate the problem into an equivalent form and prove results concerning global uniqueness and existence.