FRACTIONAL-ORDER SINE-GORDON EQUATION INVOLVING NONSINGULAR DERIVATIVE

Muhammad Sher, Aziz Khan, Kamal Shah, Thabet Abdeljawad

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)

Abstract

The sine-Gordon equation has received attention since 1970s due to the existence of soliton solutions. The aforesaid equation has significant applications in the quantum field theory. The aforementioned problem has been treated by using various numerical and analytical techniques under the ordinary as well as fractional-order derivatives. The mentioned equation has been investigated under the usual Caputo fractional-order derivative. Since in some cases the nonsingular-type derivatives produce more significant results in the mathematical modelings of real-world nonlinear problems, therefore, the proposed problem is considered in this paper under the fractional-order case in the context of Atangana-Baleanu-Caputo (ABC) derivative for the analytical and approximate results. This fractional derivative has some useful properties involving Mittag-Leffler-type kernel that is nonlocal and nonsingular. Furthermore, Modified Homotopy Perturbation Method (MHPM) is utilized for the required approximate solution. We give appropriate examples depicting the sine-Gordon model. Also, we present our results for the approximate solution graphically to support all the results.

Original languageEnglish
Article number2340007
JournalFractals
Volume31
Issue number10
DOIs
Publication statusPublished - 2023
Externally publishedYes

Keywords

  • ABC Fractional-Order Derivative
  • Modified Homotopy Perturbation Method
  • Sine-Gordon Equations

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