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arXiv · 2105.05040

Inverse problems for diffusion equation with fractional Dzherbashian-Nersesian operator

Anwar Ahmad·Muhammad Ali·Salman A. Malik
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Abstract

Fractional Dzherbashian-Nersesian operator is considered and three famous fractional order derivatives namely Riemann-Liouville, Caputo and Hilfer derivatives 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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Anwar Ahmad, Muhammad Ali, Salman A. Malik. 2021-05-09. Inverse problems for diffusion equation with fractional Dzherbashian-Nersesian operator. https://doi.org/10.1515/fca-2021-0082

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