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An inverse problem for a multi‐term fractional differential equation with two‐parameter fractional derivatives in time and Bessel operator
Author(s) -
Samreen Arifa,
Malik Salman A.
Publication year - 2021
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.7378
Subject(s) - mathematics , fractional calculus , bessel function , mathematical analysis , laplace transform , differential equation , eigenfunction , term (time) , eigenvalues and eigenvectors , physics , quantum mechanics
In this work, we investigate unique solvability of inverse source problem (ISP) of determining a time‐dependent source term along with solution for a multi‐term fractional differential equation involving two‐parameter fractional derivative in time usually known as Hilfer fractional derivative. We applied the eigenfunction expansion method, and the corresponding spectral problem consists of Bessel differential equation in space variable. The multi‐term fractional order differential equations are solved by Laplace transform and solution involve multinomial Mittag–Leffler type functions. Banach fixed‐point theorem is used to prove unique existence of time‐dependent source term whenever integral type over‐determination condition is given. Some examples are provided to support our analysis.