Fractional differential equations with Atangana–Baleanu fractional derivative: Analysis and applications

M. I. Syam, Mohammed Al-Refai

Research output: Contribution to journalArticlepeer-review

38 Citations (Scopus)

Abstract

We study linear and nonlinear fractional differential equations of order 0 < α < 1, involving the Atangana–Baleanu fractional derivative. We establish existence and uniqueness results to the linear and nonlinear problems using Banach fixed point theorem. We then develop a numerical technique based on the Chebyshev collocation method to solve the problem. As an important application we consider the fractional Riccati equation. Two examples are presented to test the efficiency of the proposed technique, where a notable agreement between the approximate and the exact solutions is obtained. Also, the approximate solutions approach to the exact solutions of the corresponding ordinary differential equations as the fractional derivative approaches 1.

Original languageEnglish
Article number100013
JournalChaos, Solitons and Fractals: X
Volume2
DOIs
Publication statusPublished - Jun 2019
Externally publishedYes

Keywords

  • Atangana–Baleanu derivative
  • Banach fixed point theorem
  • Chebyshev fractional functions
  • Collocation method
  • Fractional differential equations
  • Riccati equation

ASJC Scopus subject areas

  • Mathematics(all)

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