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

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 selfadjoint operators. We are especially interested in proving existence and uniqueness of the solutions in the abstract setting of Hilbert spaces.

A hybrid regularization method for identifying the source term and the initial value simultaneously for fractional pseudo-parabolic equations with involution *

“…At present, the problem of fractional pseudo-parabolic equations with involution has become the subject of extensive research in various mathematical models. In [9], Ruzhansky et al used L-Fourier method to obtain the uniqueness and stability of the solution of fractional involution pseudo-parabolic equations in an abstract set of Hilbert Spaces. In [10], Serikbaev used L-Fourier method to obtain the classical and generalized solutions of fractional involution inverse problems on Sobolev space, and proved the existence and uniqueness.…”

Inverse source problem for the pseudoparabolic equation associated with the Jacobi operator

“…The authors showed the existence, uniqueness, and regularity of a weak solution (u, h) ([10, Theorem 2.1, p. 1658]). One of the recent papers for ISPs for pseudoparabolic equations with fractional derivatives is [11] (in 2021). In [11], the authors considered the solvability of the ISP for the pseudoparabolic equation with the Caputo fractional derivative D α t , of order 0 < α ≤ 1,…”

Direct and inverse problems for time-fractional heat equation generated by Dunkl operator

“…, where operators L and M are operators with the corresponding discrete spectra {λ ξ } ξ∈I and {µ ξ } ξ∈I on H. In [RSTT22] well-posedness of direct and inverse problems are obtained. The difference between our work and this particular work is that we consider an ISP for the pseudo-parabolic equation associated with the Dunkl operator, which is an operator with continuous spectrum.…”