Inverse problems for diffusion equation with fractional Dzherbashian-Nersesian operator

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.

References in corpus (3)

• No Nonlocality. No Fractional Derivative
• Fractional derivatives and the fundamental theorem of Fractional Calculus
• Local Fractional Derivatives of Differentiable Functions are Integer-order Derivatives or Zero

Cited by in corpus (3)

• A boundary-value problem for a mixed type equation involving hyper-Bessel fractional differential operator and Hilfer's bi-ordinal fractional derivative
• Non-local boundary value problem for a mixed-type equation involving the bi-ordinal Hilfer fractional differential operators
• Unraveling Forward and Backward Source Problems for a Nonlocal Integrodifferential Equation: A Journey through Operational Calculus for Dzherbashian-Nersesian Operator