Hermite solution for a new fractional inverse differential problem

Mathematics, mathematical modeling of real systems, and mathematical and computer methodologies aimed at the qualitative and quantitative study of real physical systems interact in a nontrivial way. This work aims to examine a new class of inverse problems for a fractional partial differential equation with order fractional , which leads to the spectral problem involving Hermite's differential equation. We introduce proven theorems on the existence and uniqueness of solutions to the current problem. We obtain solutions in the form of series expansion using the Hermite orthogonal basis. Finally, we discuss the convergence analysis of the obtained solutions.