Abstract
PurposeFractional order nonlinear evolution equations (FNLEEs) pertaining to conformable fractional derivative are considered to be revealed for well-furnished analytic solutions due to their importance in the nature of real world. In this article, the autors suggest a productive technique, called the rational fractional (DξαG/G)-expansion method, to unravel the nonlinear space-time fractional potential Kadomtsev–Petviashvili (PKP) equation, the nonlinear space-time fractional Sharma–Tasso–Olver (STO) equation and the nonlinear space-time fractional Kolmogorov–Petrovskii–Piskunov (KPP) equation. A fractional complex transformation technique is used to convert the considered equations into the fractional order ordinary differential equation. Then the method is employed to make available their solutions. The constructed solutions in terms of trigonometric function, hyperbolic function and rational function are claimed to be fresh and further general in closed form. These solutions might play important roles to depict the complex physical phenomena arise in physics, mathematical physics and engineering.Design/methodology/approachThe rational fractional (DξαG/G)-expansion method shows high performance and might be used as a strong tool to unravel any other FNLEEs. This method is of the form U(ξ)=∑i=0nai(DξαG/G)i/∑i=0nbi(DξαG/G)i.FindingsAchieved fresh and further abundant closed form traveling wave solutions to analyze the inner mechanisms of complex phenomenon in nature world which will bear a significant role in the of research and will be recorded in the literature.Originality/valueThe rational fractional (DξαG/G)-expansion method shows high performance and might be used as a strong tool to unravel any other FNLEEs. This method is newly established and productive.
Highlights
Fractional calculus originating from some speculations of Leibniz and L’Hospital in 1695 has gradually gained profound attention of many researchers for its extensive appearance in various fields of real world
We offer a newly established technique, called the rational fractional ðDξαG=GÞ-expansion method [42], to investigate closed form analytic wave solutions to some fractional order nonlinear evolution equations (FNLEEs) in the sense of conformable fractional derivative [43]
2.2 Methodology In this subsection, we discuss the main steps of the rational fractional ðDξαG=GÞ-expansion method to examine exact traveling wave solutions to FNLEEs
Summary
Fractional calculus originating from some speculations of Leibniz and L’Hospital in 1695 has gradually gained profound attention of many researchers for its extensive appearance in various fields of real world. Exact traveling wave solutions to fractional order nonlinear evolution equations (FNLEEs) are of fundamental and important in applied science because of their wide use to depict the nonlinear fractional phenomena and dynamical processes of nature world. The FNLEEs and their solutions in closed form play fundamental role in describing, modeling and predicting the underlying mechanisms related to the biology, bio-genetics, JEL Classification — 34A08, 35R11 © Tarikul Islam and Armina Akter. Published in Arab Journal of Mathematical Sciences. The full terms of this licence may be seen at http://creativecommons.org/licences/by/4.0/ legalcode
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