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Based on a fractional subequation and the properties of the modified Riemann-Liouville fractional derivative, we propose a new analytical method named extended fractional (DξαG/G)-expansion method for seeking traveling wave solutions of fractional partial differential equations. To illustrate the effectiveness of the method, we discuss a space-time fractional Fokas equation, many types of exact analytical solutions are obtained, and the solutions include hyperbolic function and trigonometric and negative exponential solutions

mathematical problems in engineering

The Extended Fractional <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mo stretchy="false">(</mml:mo><mml:msubsup><mml:mrow><mml:mi>D</mml:mi></mml:mrow><mml:mrow><mml:mi>ξ</mml:mi></mml:mrow><mml:mrow><mml:mi>α</mml:mi></mml:mrow></mml:msubsup><mml:mi>G</mml:mi><mml:mo>/</mml:mo><mml:mi>G</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>-Expansion Method and Its Applications to a Space-Time Fractional Fokas Equation

The Extended Fractional (DξαG/G)-Expansion Method and Its Applications to a Space-Time Fractional Fokas Equation