A numerical algorithm in reproducing kernel-based approach for solving the inverse source problem of the time–space fractional diffusion equation

In this analysis, a numerical algorithm in the RKHS approach is utilized to the inverse source problem for the diffusion equation in a time–space fractional sense, where determinations of state variable and source parameter subject to initial–boundary and overdetermination conditions are the main go...

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Bibliographic Details
Published in:Partial differential equations in applied mathematics : a spin-off of Applied Mathematics Letters Vol. 4; p. 100164
Main Authors: Djennadi, Smina, Shawagfeh, Nabil, Abu Arqub, Omar
Format: Journal Article
Language:English
Published: Elsevier B.V 01.12.2021
Elsevier
Subjects:
Fractional diffusion equation
Fractional partial differential equations
Inverse source problem
Reproducing kernel Hilbert space
Source parameter
State variable
NPS
RKHS
Reproducing kernel Hilbert space
Inverse source problem
FDE
ISP
FPDE
Fractional diffusion equation
Source parameter
IBC
Fractional partial differential equations
State variable
ISSN:2666-8181, 2666-8181
Online Access:Get full text
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Summary:In this analysis, a numerical algorithm in the RKHS approach is utilized to the inverse source problem for the diffusion equation in a time–space fractional sense, where determinations of state variable and source parameter subject to initial–boundary and overdetermination conditions are the main goal. Consequently, specifics theoretical demonstrations are presented to interpret the NPSs to such a fractional problem. In this direction, convergence analysis and error estimates of the developed approach are studied and analyzed as well. Concerning the considered equation, specific unidirectional physical experiments are given in a finite compact regime to confirm the theoretical aspects and to demonstrate the superiority of the utilized approach. Some representative results are presented in two-dimensional graphs, whilst dynamic behaviors of fractional parameters are reported for several fixed α,β values. From the practical viewpoint, the archived simulations and consequences justify that the iterative approach is a straightforward and appropriate tool with computational efficiency for numeric solutions of the inverse source problem. •The RKHS approach is utilized to ISP of the diffusion equation in a fractional sense.•Specifics theoretical results are given to interpret the NPSs to such fractional ISP.•Convergence analysis and error estimates of the RKHS algorithm are studied.•Representative dynamic behavior results are reported in terms of graphs and tables.
ISSN:2666-8181
2666-8181
DOI:10.1016/j.padiff.2021.100164