A boundary problem for the time-fractional Hallaire–Luikov moisture transfer equation with Hilfer derivative

Al-Salti, Nasser; Karimov, Erkinjon; Kerbal, Sebti

doi:10.1007/s40314-023-02231-y

Search citation statements

Order By: Relevance

Paper Sections

Select...

Introduction and Problems Statement1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2024

Publication Types

Select...

Article1

Relationship

Self Cite0

Independent1

Authors

Journals

Cited by 1 publication

(1 citation statement)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…These kind of problems have also been studied for fractional diffusion equations in [16][17][18]. Recently, backward problems for FDEs involving Caputo and generalized Riemann-Liouville derivatives have been extensively studied [19][20][21]. However, there is a limited body of literature pertaining to the forward and backward problems associated with FDEs that feature the Dzherbashian-Nersesian operator.…”

Section: Introduction and Problems Statementmentioning

confidence: 99%

Unraveling forward and backward source problems for a nonlocal integrodifferential equation: A journey through operational calculus for Dzherbashian‐Nersesian operator

Ahmad,

Ali,

Malik

2024

Math Methods in App Sciences

View full text Add to dashboard Cite

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 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. Solutions are presented using Mittag‐Leffler (ML) type functions. The outcomes related to the existence and uniqueness subject to certain conditions of regularity on the input data are developed.

show abstract