A fractional derivative with two singular kernels and application to a heat conduction problem

Dumitru Baleanu; Mohamed Jleli; Sunil Kumar; Bessem Samet

doi:10.1186/s13662-020-02684-z

A fractional derivative with two singular kernels and application to a heat conduction problem

Dumitru Baleanu
, Mohamed Jleli
, Sunil Kumar
, Bessem Samet

Cankaya University
China Medical University Taichung
Institute for Space Sciences
King Saud University
National Institute of Technology

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

63 Scopus citations

Abstract

In this article, we suggest a new notion of fractional derivative involving two singular kernels. Some properties related to this new operator are established and some examples are provided. We also present some applications to fractional differential equations and propose a numerical algorithm based on a Picard iteration for approximating the solutions. Finally, an application to a heat conduction problem is given.

Original language	English
Article number	252
Journal	Advances in Difference Equations
Volume	2020
Issue number	1
DOIs	https://doi.org/10.1186/s13662-020-02684-z
State	Published - 1 Dec 2020
Externally published	Yes

Keywords

Fractional derivative
Heat conduction problem
Picard iteration
Two singular kernels

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10.1186/s13662-020-02684-z

Cite this

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abstract = "In this article, we suggest a new notion of fractional derivative involving two singular kernels. Some properties related to this new operator are established and some examples are provided. We also present some applications to fractional differential equations and propose a numerical algorithm based on a Picard iteration for approximating the solutions. Finally, an application to a heat conduction problem is given.",

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AU - Baleanu, Dumitru

AU - Jleli, Mohamed

AU - Kumar, Sunil

AU - Samet, Bessem

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N2 - In this article, we suggest a new notion of fractional derivative involving two singular kernels. Some properties related to this new operator are established and some examples are provided. We also present some applications to fractional differential equations and propose a numerical algorithm based on a Picard iteration for approximating the solutions. Finally, an application to a heat conduction problem is given.

AB - In this article, we suggest a new notion of fractional derivative involving two singular kernels. Some properties related to this new operator are established and some examples are provided. We also present some applications to fractional differential equations and propose a numerical algorithm based on a Picard iteration for approximating the solutions. Finally, an application to a heat conduction problem is given.

KW - Fractional derivative

KW - Heat conduction problem

KW - Picard iteration

KW - Two singular kernels

UR - https://www.scopus.com/pages/publications/85085470259

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DO - 10.1186/s13662-020-02684-z

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JO - Advances in Difference Equations

JF - Advances in Difference Equations

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A fractional derivative with two singular kernels and application to a heat conduction problem

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Keywords

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