IDENTIFICATION OF A TIME-DEPENDENT SOURCE TERM IN A NONLOCAL PROBLEM FOR TIME FRACTIONAL DIFFUSION EQUATION-Reference-Cited by-同舟云学术

IDENTIFICATION OF A TIME-DEPENDENT SOURCE TERM IN A NONLOCAL PROBLEM FOR TIME FRACTIONAL DIFFUSION EQUATION

Published:2024-03-26 Issue:2 Volume:29 Page:238-253
ISSN:1392-6292
Container-title:Mathematical Modelling and Analysis
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Author:

Ismailov Mansur I.¹,Çiçek Muhammed²^ORCID

Affiliation:

1. Department of Mathematics, Gebze Technical University, 41400 Gebze, Kocaeli, Turkey; Department of Mathematics, Khazar University, AZ1096 Baku, Azerbaijan

2. Department of Mathematics, Khazar University, AZ1096 Baku, Azerbaijan

Abstract

This paper is concerned with the inverse problem of recovering the time dependent source term in a time fractional diffusion equation, in the case of nonlocal boundary condition and integral overdetermination condition. The boundary conditions of this problem are regular but not strongly regular. The existence and uniqueness of the solution are established by applying generalized Fourier method based on the expansion in terms of root functions of a spectral problem, weakly singular Volterra integral equation and fractional type Gronwall’s inequality. Moreover, we show its continuous dependence on the data.

Publisher

Vilnius Gediminas Technical University

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