Progress in Fractional Differentiation & Applications

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The present paper aims to investigate the numerical solutions of the seventh order Caputo fractional time Kaup-Kupershmidt, Sawada-Kotera and Lax’s Korteweg-de Vries equations using two reliable techniques, namely, the fractional reduced differential transform method and q-homotopy analysis transform method. These equations are the mathematical formulation of physical phenomena that arise in chemistry, engineering and physics. For instance, in the motions of long waves in shallow water under gravity, nonlinear optics, quantum mechanics, plasma physics, fluid mechanics and so on. With these two methods, we construct series solution to these problems in the recurrence relation form. We present error estimates to further investigate the accuracy and reliability of the proposed techniques. The outcome of the study reveals that the two techniques used are computationally accurate, reliable and easy to implement when solving fractional nonlinear complex phenomena that arise in physics, biology, chemistry and mathematics.

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