Article

An Inverse Problem of Determining the Kernel of a Fractional Pseudo-Integro-Differential Equation

D. K. DurdievBukhara Branch of Romanovskiy Institute of Mathematcs of the Academy of Sciences of Uzbekistan, 200100, Bukhara, UzbekistanH. B. ElmuradovaBukhara State University, 200100, Bukhara, Uzbekistan

Lobachevskii Journal of Mathematicsjournal2025en

ABI

Abstract

In this work, the kernel determination inverse problem with initial-boundary and over-determination conditions for a pseudoparabolic integrodifferential equation involving fractional Caputo derivative is studied. First, an equivalent auxiliary problem is reduced. Investigation of the direct problem is conducted by the Fourier method. The inverse problem reduces to solving a Volterra type integral equation of the second kind with respect to an unknown function. Using the fixed point theorem, the unique solvability of the inverse problem is proven for a sufficiently small segment.

Topics

Differential Equations and Boundary Problems Fractional Differential Equations Solutions Differential Equations and Numerical Methods

Identifiers

DOI: 10.1134/s1995080225605399

Citations and references

Cited by 038 references

Metrics — AkademScholar · Coming soon