An inverse problem for a multi‐term fractional differential equation with two‐parameter fractional derivatives in time and Bessel operator

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 ap...

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Bibliographic Details
Published inMathematical methods in the applied sciences Vol. 44; no. 11; pp. 9541 - 9556
Main Authors Samreen, Arifa, Malik, Salman A.
Format Journal Article
LanguageEnglish
Published Freiburg Wiley Subscription Services, Inc 30.07.2021
Subjects
Bessel operator
Derivatives
Differential equations
Eigenvectors
Existence theorems
Inverse problems
inverse source problem
Laplace transforms
multinomial Mittag–Leffler function
Operators (mathematics)
Parameters
Time dependence
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Summary: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.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.7378