Inverse problem for a multi-parameters space-time fractional diffusion equation with nonlocal boundary conditions: operational calculus approach

2021 ◽  
Vol 13 (1) ◽  
Author(s):  
Muhammad Ali ◽  
Sara Aziz ◽  
Salman A. Malik
Keyword(s):  
Inverse Problem ◽  
Diffusion Equation ◽  
Boundary Conditions ◽  
Nonlocal Boundary ◽  
Operational Calculus ◽  
Nonlocal Boundary Conditions ◽  
Fractional Diffusion ◽  
Space Time ◽  
Fractional Diffusion Equation ◽  
Time Fractional Diffusion Equation

scholarly journals SIMULTANEOUS DETERMINATION OF A SOURCE TERM AND DIFFUSION CONCENTRATION FOR A MULTI-TERM SPACE-TIME FRACTIONAL DIFFUSION EQUATION

2021 ◽  
Vol 26 (3) ◽  
pp. 411-431
Author(s):  
Salman A. Malik ◽  
Asim Ilyas ◽  
Arifa Samreen
Keyword(s):  
Inverse Problem ◽  
Diffusion Equation ◽  
Source Term ◽  
Fractional Diffusion ◽  
Adjoint Problem ◽  
Space Time ◽  
Fractional Diffusion Equation ◽  
Diffusion Temperature ◽  
Non Local ◽  
Time Fractional Diffusion Equation

An inverse problem of determining a time dependent source term along with diffusion/temperature concentration from a non-local over-specified condition for a space-time fractional diffusion equation is considered. The space-time fractional diffusion equation involve Caputo fractional derivative in space and Hilfer fractional derivatives in time of different orders between 0 and 1. Under certain conditions on the given data we proved that the inverse problem is locally well-posed in the sense of Hadamard. Our method of proof based on eigenfunction expansion for which the eigenfunctions (which are Mittag-Leffler functions) of fractional order spectral problem and its adjoint problem are considered. Several properties of multinomial Mittag-Leffler functions are proved.

Sign in / Sign up

Export Citation Format

Share Document