Abstract
AbstractIn this paper, the new exact solutions of nonlinear conformable fractional partial differential equations(CFPDEs) are achieved by using auxiliary equation method for the nonlinear space-time fractional Klein-Gordon equation and the (2+1)-dimensional time-fractional Zoomeron equation. The technique is easily applicable which can be applied successfully to get the solutions for different types of nonlinear CFPDEs. The conformable fractional derivative(CFD) definitions are used to cope with the fractional derivatives.
Highlights
Fractional calculus first started in 1600s, with the question of G.W
The conformable derivative definition is newly defined by Khalil and et al [6], which is very closer to definition of general calculus
First we examine the exact solutions of the space-time nonlinear fractional Klein-Gordon equation, which is well known, linear and nonlinear Klein–Gordon equations model many problems in classical and quantum mechanics, solitons, and condensed matter physics [23,27,28]
Summary
Fractional calculus first started in 1600s, with the question of G.W. Leibnitz, can integer-order derivative be generalized for non-integer derivatives?, to L’Hospital [1]. The conformable derivative definition is newly defined by Khalil and et al [6], which is very closer to definition of general calculus. We observe the (2+1) dimensional time-fractional Zoomeron Equation, which is a convenient model to display the novel phenomena associated with boomerons and trappons is studied [29, 30]. These two equations have been solved using different methods before and we have found new exact solutions by using the auxiliary equation method.
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