Fundamental results on weighted Caputo–Fabrizio fractional derivative

Moh'd Abdalla Oglah Alrefai, Abdulla M. Jarrah

Research output: Contribution to journalArticlepeer-review

26 Citations (Scopus)

Abstract

In this paper, we define the weighted Caputo–Fabrizio fractional derivative of Caputo sense, and study related linear and nonlinear fractional differential equations. The solution of the linear fractional differential equation is obtained in a closed form, and has been used to define the weighted Caputo–Fabrizio fractional integral. We study main properties of the weighted Caputo–Fabrizio fractional derivative and integral. We also, apply the Banach fixed point theorem to establish the existence of a unique solution to the nonlinear fractional differential equation. Two examples are presented to illustrate the efficiency of the obtained results.

Original languageEnglish
Pages (from-to)7-11
Number of pages5
JournalChaos, Solitons and Fractals
Volume126
DOIs
Publication statusPublished - Sep 1 2019
Externally publishedYes

Keywords

  • Caputo–Fabrizio fractional derivative
  • Fractional differential equations
  • Weighted fractional derivatives

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematics(all)
  • Physics and Astronomy(all)
  • Applied Mathematics

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