Abstract
The phenomena, molecular path in a liquid or a gas, fluctuating price stoke, fission and fusion, quantum field theory, relativistic wave motion, etc., are modeled through the nonlinear time fractional clannish random Walker’s parabolic (CRWP) equation, nonlinear time fractional SharmaTassoOlver (STO) equation, and the nonlinear space-time fractional KleinGordon equation. The fractional derivative is described in the sense of conformable derivative. From there, the G ′ / G , 1 / G -expansion method is found to be ensuing, effective, and capable to provide functional solutions to nonlinear models concerning physical and engineering problems. In this study, an extension of the G ′ / G , 1 / G -expansion method has been introduced. This enhancement establishes broad-ranging and adequate fresh solutions. In addition, some existing solutions attainable in the literature also confirm the validity of the suggested extension. We believe that the extension might be added to the literature as a reliable and efficient technique to examine a wide variety of nonlinear fractional systems with parameters including solitary and periodic wave solutions to nonlinear FDEs.
Highlights
Conformable Fractional Derivative and Its Important PropertiesKhalil et al [4] introduced a simple, interesting, and compatible with typical definition of derivative named conformable fractional derivative, which can rectify the deficiencies of the other definitions
Introduction e subjectFDEs can be considered as a generalization of the typical ordinary differential equations (ODEs). e advantages of the FDEs become apparent for us to understand real world problems
We will suggest an extension of the (G′/G, 1/G)-expansion method to ascertain the analytic solutions to nonlinear FDEs
Summary
Khalil et al [4] introduced a simple, interesting, and compatible with typical definition of derivative named conformable fractional derivative, which can rectify the deficiencies of the other definitions. One can find several useful studies related to this new definition in [5,6,7,8]. In [39], the geometrical and physical interpretations of this definition are investigated and the potential applications in science and engineering are pointer out. E conformable fractional derivative of a function g of order β is defined as gt + x t1− β − g(t). Some important properties of above definition are given below:
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