Reduction of order formula and fundamental set of solutions for linear fractional differential equations

Mohammed Al-Refai

doi:10.1016/j.aml.2018.02.014

Reduction of order formula and fundamental set of solutions for linear fractional differential equations

Mohammed Al-Refai

Department of Mathematical Sciences

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

12 Citations (Scopus)

Abstract

In this paper, we consider a class of linear fractional differential equations involving the Caputo–Fabrizio fractional derivative of order 1<α<2. We derive, in closed form, a reduction of order formula to obtain a second linearly independent solution. We then establish a fundamental set of solutions result to the equation. One example is presented to illustrate the validity of the obtained results.

Original language	English
Pages (from-to)	8-13
Number of pages	6
Journal	Applied Mathematics Letters
Volume	82
DOIs	https://doi.org/10.1016/j.aml.2018.02.014
Publication status	Published - Aug 2018

Keywords

Caputo–Fabrizio fractional derivative
Fractional differential equations
Fundamental solutions set

ASJC Scopus subject areas

Applied Mathematics

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10.1016/j.aml.2018.02.014

Cite this

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title = "Reduction of order formula and fundamental set of solutions for linear fractional differential equations",

abstract = "In this paper, we consider a class of linear fractional differential equations involving the Caputo–Fabrizio fractional derivative of order 1<α<2. We derive, in closed form, a reduction of order formula to obtain a second linearly independent solution. We then establish a fundamental set of solutions result to the equation. One example is presented to illustrate the validity of the obtained results.",

keywords = "Caputo–Fabrizio fractional derivative, Fractional differential equations, Fundamental solutions set",

author = "Mohammed Al-Refai",

note = "Publisher Copyright: {\textcopyright} 2018 Elsevier Ltd",

year = "2018",

month = aug,

doi = "10.1016/j.aml.2018.02.014",

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AU - Al-Refai, Mohammed

PY - 2018/8

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N2 - In this paper, we consider a class of linear fractional differential equations involving the Caputo–Fabrizio fractional derivative of order 1<α<2. We derive, in closed form, a reduction of order formula to obtain a second linearly independent solution. We then establish a fundamental set of solutions result to the equation. One example is presented to illustrate the validity of the obtained results.

AB - In this paper, we consider a class of linear fractional differential equations involving the Caputo–Fabrizio fractional derivative of order 1<α<2. We derive, in closed form, a reduction of order formula to obtain a second linearly independent solution. We then establish a fundamental set of solutions result to the equation. One example is presented to illustrate the validity of the obtained results.

KW - Caputo–Fabrizio fractional derivative

KW - Fractional differential equations

KW - Fundamental solutions set

UR - https://www.scopus.com/pages/publications/85043282539

UR - https://www.scopus.com/pages/publications/85043282539#tab=citedBy

U2 - 10.1016/j.aml.2018.02.014

DO - 10.1016/j.aml.2018.02.014

M3 - Article

AN - SCOPUS:85043282539

SN - 0893-9659

VL - 82

SP - 8

EP - 13

JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

ER -

Reduction of order formula and fundamental set of solutions for linear fractional differential equations

Abstract

Keywords

ASJC Scopus subject areas

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