Fundamental results on weighted Caputo–Fabrizio fractional derivative

Mohammed Al-Refai and Abdulla M. Jarrah

Chaos, Solitons & Fractals, 2019, vol. 126, issue C, 7-11

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.

Keywords: Weighted fractional derivatives; Caputo–Fabrizio fractional derivative; Fractional differential equations (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:126:y:2019:i:c:p:7-11

DOI: 10.1016/j.chaos.2019.05.035

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