On Recovering a Time-dependent Inverse Problem in the Diffusion Model with a Dirichlet-type Constraint and an Integral Overposed Condition: Theory and Simulation

Our aim in this paper is to recover a time-dependent source term, along with the solution of the diffusion equation, by using a new definition of the derivative, known as the conformable approach. Herein, the inverse problem is utilized subject to Dirichlet boundary constraint conditions and an integral overposed condition. An explicit solution in series form for the considered inverse source problem is obtained by employing the Fourier expansion scheme. The thoughtful mathematical structure, including the theoretical (existence, stability, and uniqueness) for the suggested regular solution, is settled and affirmed. Two time-conformable diffusion equation examples are considered to show the stability result. Various graphical plots and numerical tables are utilized to confirm the results discussed. The final remarks, highlights, and some focused references are given at the end.