Application of the Simple Equation Method with Jumarie’s Modified Riemann–Liouville Derivative to Space–Time Fractional Nonlinear mBBM and ZKBBM
Keywords:
Space-time fractional mBBM equation, Space-time fractional ZKBBM equation, Simple equation method, Jumarie’s modified Riemann-Liouville fractional derivative, Kink waveAbstract
This paper employs the Simple Equation (SE) method in conjunction with Jumarie’s modified Riemann–Liouville fractional derivative to derive exact solutions for the space–time fractional modified Benjamin–Bona–Mahony (mBBM) and Zakharov–Kuznetsov Benjamin–Bona–Mahony (ZKBBM) equations. The obtained exponential-type solutions describe kink-shaped traveling waves, which are illustrated through 2D, 3D, and contour plots using suitable parameters. The results confirm the efficiency and reliability of the proposed method as a robust analytical technique for deriving traveling wave solutions in nonlinear fractional models encountered in science and engineering. This study extends the SE method within the framework of Jumarie’s modified Riemann–Liouville fractional derivative, broadening its applicability to space–time fractional systems. The approach establishes a new analytical framework for fractional traveling wave solutions, and the derived results uncover additional dynamical behaviors of the mBBM and ZKBBM equations, demonstrating both the originality and effectiveness of the proposed method.
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