Identification of a time-dependent source term in a nonlocal problem for time fractional diffusion equation

• Published in: Mathematical modelling and analysis Vol. 29; no. 2; pp. 238 - 253
• Main Authors: Ismailov, Mansur I., Çiçek, Muhammed
• Format: Journal Article
• Language: English
• Published: Vilnius Vilnius Gediminas Technical University 26.03.2024
• Subjects: Analysis; Boundary conditions; Boundary value problems; Dissolution; Eigenvalues; Energy; fractional diffusion equation; Functions, Inverse; generalized Fourier method; Heat; Heat equation; Identification; Integral equations; Inverse problems; inverse source problem; Investigations; not strongly regular boundary condition; Tests, problems and exercises; Time dependence; Volterra integral equations; weakly singular Volterra integral equation; Turkey; generalized Fourier method; weakly singular Volterra integral equation; inverse source problem; not strongly regular boundary condition; fractional diffusion equation
• ISSN: 1392-6292; 1648-3510
• DOI: 10.3846/mma.2024.17791

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.