Initial boundary value problems for a fractional differential equation with hyper-Bessel operator

Fatma Al-Musalhi, Nasser Al-Salti, Erkinjon Karimov

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

Direct and inverse source problems of a fractional diffusion equation with regularized Caputo-like counterpart of a hyper-Bessel differential operator are considered. Solutions to these problems are constructed based on appropriate eigenfunction expansions and results on existence and uniqueness are established. To solve the resultant equations, a solution to such kind of non-homogeneous fractional differential equation is also presented.

Original languageEnglish
Pages (from-to)200-219
Number of pages20
JournalFractional Calculus and Applied Analysis
Volume21
Issue number1
DOIs
Publication statusPublished - Feb 23 2018

Fingerprint

Bessel Operator
Inverse Source Problem
Fractional Diffusion Equation
Eigenfunction Expansion
Fractional Differential Equation
Eigenvalues and eigenfunctions
Initial-boundary-value Problem
Boundary value problems
Mathematical operators
Differential operator
Existence and Uniqueness
Differential equations

Keywords

  • Erdélyi-Kober fractional order operators
  • fractional differential equations
  • hyper-Bessel operators
  • initial boundary value problems
  • inverse problems
  • Mittag-Leffler functions
  • series solutions

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

Initial boundary value problems for a fractional differential equation with hyper-Bessel operator. / Al-Musalhi, Fatma; Al-Salti, Nasser; Karimov, Erkinjon.

In: Fractional Calculus and Applied Analysis, Vol. 21, No. 1, 23.02.2018, p. 200-219.

Research output: Contribution to journalArticle

@article{b357a9c49eec427a9105c219e577d42e,
title = "Initial boundary value problems for a fractional differential equation with hyper-Bessel operator",
abstract = "Direct and inverse source problems of a fractional diffusion equation with regularized Caputo-like counterpart of a hyper-Bessel differential operator are considered. Solutions to these problems are constructed based on appropriate eigenfunction expansions and results on existence and uniqueness are established. To solve the resultant equations, a solution to such kind of non-homogeneous fractional differential equation is also presented.",
keywords = "Erd{\'e}lyi-Kober fractional order operators, fractional differential equations, hyper-Bessel operators, initial boundary value problems, inverse problems, Mittag-Leffler functions, series solutions",
author = "Fatma Al-Musalhi and Nasser Al-Salti and Erkinjon Karimov",
year = "2018",
month = "2",
day = "23",
doi = "10.1515/fca-2018-0013",
language = "English",
volume = "21",
pages = "200--219",
journal = "Fractional Calculus and Applied Analysis",
issn = "1311-0454",
publisher = "Springer Science + Business Media",
number = "1",

}

TY - JOUR

T1 - Initial boundary value problems for a fractional differential equation with hyper-Bessel operator

AU - Al-Musalhi, Fatma

AU - Al-Salti, Nasser

AU - Karimov, Erkinjon

PY - 2018/2/23

Y1 - 2018/2/23

N2 - Direct and inverse source problems of a fractional diffusion equation with regularized Caputo-like counterpart of a hyper-Bessel differential operator are considered. Solutions to these problems are constructed based on appropriate eigenfunction expansions and results on existence and uniqueness are established. To solve the resultant equations, a solution to such kind of non-homogeneous fractional differential equation is also presented.

AB - Direct and inverse source problems of a fractional diffusion equation with regularized Caputo-like counterpart of a hyper-Bessel differential operator are considered. Solutions to these problems are constructed based on appropriate eigenfunction expansions and results on existence and uniqueness are established. To solve the resultant equations, a solution to such kind of non-homogeneous fractional differential equation is also presented.

KW - Erdélyi-Kober fractional order operators

KW - fractional differential equations

KW - hyper-Bessel operators

KW - initial boundary value problems

KW - inverse problems

KW - Mittag-Leffler functions

KW - series solutions

UR - http://www.scopus.com/inward/record.url?scp=85044303294&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85044303294&partnerID=8YFLogxK

U2 - 10.1515/fca-2018-0013

DO - 10.1515/fca-2018-0013

M3 - Article

AN - SCOPUS:85044303294

VL - 21

SP - 200

EP - 219

JO - Fractional Calculus and Applied Analysis

JF - Fractional Calculus and Applied Analysis

SN - 1311-0454

IS - 1

ER -