Recovering Source Term and Temperature Distribution for Nonlocal Heat Equation

Identifying temperature distribution and source term for generalized diffusion equation with arbitrary memory kernel

“…We have already obtained uniqueness of the source term q(t) by using Banach fixed point theorem. v(x, t) can be proved by considering v 1 (x, t) and v 2 (x, t) as the two regular solution set of the ISP-II (1)-( 5) and (7), and finding them equal, that is, v 1 (x, t) = v 2 (x, t) by using the fact that bi-orthogonal systems of functions ( 14) form a complete set in L 2 ((0, 1)). □…”

“…ISPs for a diffusion equations with nonlocal boundary conditions are studied, see [7,8]. The nonlocal boundary conditions arise in many physical phenomena, see, for example, [9][10][11].…”

“…This motivates the exploration and investigation of nonlocal boundary‐value problems. ISPs for a diffusion equations with nonlocal boundary conditions are studied, see [7, 8]. The nonlocal boundary conditions arise in many physical phenomena, see, for example, [9–11].…”

On the solvability of direct and inverse problems for a generalized diffusion equation

“…Several properties of the Dzherbashian-Nersesian FD have been proved in Ahmad et al [12]. In Asim et al [13,14], FOOs usually Know as nth level FD has been shown to be generalization of well-known functions such as HFD, CFD and RFD and ISPs for a time-fractional diffusion equations (TFDEs) with nth level FD are considered. DPs for diffusion equations involving non-classical BCs are studied in the works [15][16][17].…”