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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Ahmad, A., Ali, M. & Malik, S.A. Inverse Problems for Diffusion Equation with Fractional Dzherbashian-Nersesian Operator. Fract Calc Appl Anal 24, 1899–1918 (2021). https://doi.org/10.1515/fca-2021-0082
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DOI: https://doi.org/10.1515/fca-2021-0082