Solvability of inverse problem of a pseudoparabolic equation with fractional Caputo derivative

Abstract

 Inverse problem on recovering the coefficient of the right-hand side for a pseudoparabolic equation with a Caputo fractional derivative is studied. Overdetermination condition of the inverse problem is given in integral form. Existence and uniqueness theorems are proved for regular solutions (i.e., having all Sobolev generalized derivatives entering the equation) for a pseudoparabolic equation with the Caputo fractional derivative. Also, we propose an algorithm for numerical solution of the considered inverse problem. Numerical experiments are carried out for a one-dimensional problem, illustrating the obtained theoretical results. Inverse problems with fractional derivatives belong to the class of problems that are associated with determining unknown parameters or functions in mathematical models described by equations with fractional derivatives. Such problems arise in various applications where models with fractional derivatives are used, for example, in mechanics, heat conductivity, biology, finance and other areas.