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

Autor:	Ahmad, Anwar, Ali, Muhammad, Malik, Salman A.
Rok vydání:	2023
Předmět:	Mathematics - Analysis of PDEs
Druh dokumentu:	Working Paper
DOI:	10.1002/mma.9996
Popis:	This article primarily aims at introducing a novel operational calculus of Mikusi\'nski'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. Comment: 13 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2309.14386 Zobrazit plný text záznamu View this record from Arxiv