A Cauchy-type problem with a sequential fractional derivative in the space of continuous functions

Khaled M. Furati

doi:10.1186/1687-2770-2012-58

A Cauchy-type problem with a sequential fractional derivative in the space of continuous functions

Khaled M. Furati^*

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

A Cauchy-type nonlinear problem for a class of fractional differential equations with sequential derivatives is considered in the space of weighted continuous functions. Some properties and composition identities are derived. The equivalence with the associated integral equation is established. An existence and uniqueness result of the global continuous solution is proved.

Original language	English
Article number	58
Journal	Boundary Value Problems
Volume	2012
DOIs	https://doi.org/10.1186/1687-2770-2012-58
State	Published - 2012

Bibliographical note

Funding Information:
The author was grateful for the support provided by the King Fahd University of Petroleum & Minerals and the financial support by the BAE Systems through the PDSR program by the British Council in Saudi Arabia.

Keywords

Fractional derivatives
Fractional differential equation
Riemann-Liouville fractional derivative
Sequential fractional derivative

ASJC Scopus subject areas

Analysis
Algebra and Number Theory

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10.1186/1687-2770-2012-58

Cite this

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title = "A Cauchy-type problem with a sequential fractional derivative in the space of continuous functions",

abstract = "A Cauchy-type nonlinear problem for a class of fractional differential equations with sequential derivatives is considered in the space of weighted continuous functions. Some properties and composition identities are derived. The equivalence with the associated integral equation is established. An existence and uniqueness result of the global continuous solution is proved.",

keywords = "Fractional derivatives, Fractional differential equation, Riemann-Liouville fractional derivative, Sequential fractional derivative",

author = "Furati, \{Khaled M.\}",

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AU - Furati, Khaled M.

N1 - Funding Information: The author was grateful for the support provided by the King Fahd University of Petroleum & Minerals and the financial support by the BAE Systems through the PDSR program by the British Council in Saudi Arabia.

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Y1 - 2012

N2 - A Cauchy-type nonlinear problem for a class of fractional differential equations with sequential derivatives is considered in the space of weighted continuous functions. Some properties and composition identities are derived. The equivalence with the associated integral equation is established. An existence and uniqueness result of the global continuous solution is proved.

AB - A Cauchy-type nonlinear problem for a class of fractional differential equations with sequential derivatives is considered in the space of weighted continuous functions. Some properties and composition identities are derived. The equivalence with the associated integral equation is established. An existence and uniqueness result of the global continuous solution is proved.

KW - Fractional derivatives

KW - Fractional differential equation

KW - Riemann-Liouville fractional derivative

KW - Sequential fractional derivative

UR - https://www.scopus.com/pages/publications/84866714879

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JO - Boundary Value Problems

JF - Boundary Value Problems

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ER -

A Cauchy-type problem with a sequential fractional derivative in the space of continuous functions

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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