Unraveling Forward and Backward Source Problems for a Nonlocal Integrodifferential Equation: A Journey through Operational Calculus for Dzherbashian-Nersesian Operator

Abstract

This article primarily aims at introducing a novel operational calculus of Mikusiński's type for the Dzherbashian-Nersesian operator. Using this calculus, we are able to derive exact solutions for the forward and backward source problems (BSPs) of a differential equation that features Dzherbashian-Nersesian operator in time and intertwined with nonlocal boundary conditions. The initial condition is expressed in terms of Riemann-Liouville integral (RLI). Solution is presented using Mittag-Leffler type functions (MLTFs). The outcomes related to the existence and uniqueness subject to certain conditions of regularity on the input data are established.

arXiv comment13 pages

References in corpus (3)

• Fractional derivatives and the fundamental theorem of Fractional Calculus
• Inverse problems for diffusion equation with fractional Dzherbashian-Nersesian operator
• On complete monotonicity of solution to the fractional relaxation equation with the $n$th level fractional derivative