time fractional diffusion equation
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2021 ◽  
Vol 40 ◽  
pp. 1-15
Author(s):  
Fatima Dib ◽  
Mokhtar Kirane

In this paper, we consider an inverse problem for a linear heat equation involving two time-fractional derivatives, subject to a nonlocal boundary condition. We determine a source term independent of the space variable, and the temperature distribution with an over- determining function of integral type.


2021 ◽  
Vol 24 (6) ◽  
pp. 1899-1918
Author(s):  
Anwar Ahmad ◽  
Muhammad Ali ◽  
Salman A. Malik

Abstract Fractional Dzherbashian-Nersesian operator is considered and three famous fractional order derivatives named after Riemann-Liouville, Caputo and Hilfer are shown to be special cases of the earlier one. The expression for Laplace transform of fractional Dzherbashian-Nersesian operator is constructed. Inverse problems of recovering space dependent and time dependent source terms of a time fractional diffusion equation with involution and involving fractional Dzherbashian-Nersesian operator are considered. The results on existence and uniqueness for the solutions of inverse problems are established. The results obtained here generalize several known results.


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