Direct and Inverse problems for time-fractional pseudo-parabolic equations

TL;DR

This paper investigates the solvability of direct and inverse problems for time-fractional pseudo-parabolic equations with self-adjoint operators, focusing on existence and uniqueness of solutions within Hilbert spaces.

Contribution

It establishes the existence and uniqueness results for both direct and inverse problems in an abstract Hilbert space framework for time-fractional pseudo-parabolic equations.

Findings

Proved existence of solutions for the direct problem.

Established uniqueness of solutions for the inverse problem.

Extended solvability results to a broad class of self-adjoint operators.

Abstract

The purpose of this paper is to establish the solvability results to direct and inverse problems for time-fractional pseudo-parabolic equations with the self-adjoint operators. We are especially interested in proving existence and uniqueness of the solutions in the abstract setting of Hilbert spaces.