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Modified Kawahara equation within a fractional derivative with non-singular kernel

Kumar Devendra (JECRC University, Department of Mathematics, Jaipur, Rajasthan, India)
Singh Jagdev (JECRC University, Department of Mathematics, Jaipur, Rajasthan, India)
Baleanu Dumitru (Cankaya University, Faculty of Arts and Sciences, Department of Mathematics, Etimesgut, Turkey + Institute of Space Sciences, Magurele-Bucharest, Romania)

The article addresses a time-fractional modified Kawahara equation through a fractional derivative with exponential kernel. The Kawahara equation describes the generation of non-linear water-waves in the long-wavelength regime. The numerical solution of the fractional model of modified version of Kawahara equation is derived with the help of iterative scheme and the stability of applied technique is established. In order to demonstrate the usability and effectiveness of the new fractional derivative to describe water-waves in the long-wavelength regime, numerical results are presented graphically.

Keywords: fractional model modified Kawahara equation, water waves, Caputo-Fabrizio fractional derivative, iterative method