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    Approximate Analytical Solutions of Conformable Time Fractional Clannish Random Walker’s Parabolic(CRWP) Equation and Modified Benjamin-Bona-Mahony(BBM) equation
    (Emrah Evren KARA, 2020) Atilgan, Emrah; Tasbozan, Orkun; Kurt, Ali; Mohyud-Din, Syed Tauseef
    In this paper, we propose the approximate analytical solutions of conformable time fractional Clannish Random Walker’s Parabolic(CRWP) equation and Modified Benjamin-Bona-Mahony(BBM) equation with the aid of generalized homotopy analysis method (q-HAM). The h curves of approximate solutions for both equations are illustrated by graphics to deter-mine the convergence interval. h values obtained from these graphics are used to compare approximate solutions with the analytical solutions. The results show that approximate solutions are consistent with the analytical solutions. Also it is understood that the method is reliable, applicable and efficient technique to get the exact solutions of fractional partial differential equations. © 2020, Emrah Evren KARA. All rights reserved.
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    New Wave Solutions of Time-Fractional Coupled Boussinesq-Whitham-Broer-Kaup Equation as A Model of Water Waves
    (China Ocean Press, 2019) Atilgan, Emrah; Senol, Mehmet; Kurt, Ali; Tasbozan, Orkun
    The main purpose of this paper is to obtain the wave solutions of conformable time fractional Boussinesq-Whitham-Broer-Kaup equation arising as a model of shallow water waves. For this aim, the authors employed auxiliary equation method which is based on a nonlinear ordinary differential equation. By using conformable wave transform and chain rule, a nonlinear fractional partial differential equation is converted to a nonlinear ordinary differential equation. This is a significant impact because neither Caputo definition nor Riemann-Liouville definition satisfies the chain rule. While the exact solutions of the fractional partial derivatives cannot be obtained due to the existing drawbacks of Caputo or Riemann-Liouville definitions, the reliable solutions can be achieved for the equations defined by conformable fractional derivatives.