The aim of this paper is by using the fractional complex transform and the optimal homotopy analysis by method (OHAM) to find the analytical approximate solutions for nonlinear partial fractional differential Zakharov-Kuznetsov equation. Fractional complex transformation is proposed to convert nonlinear partial fractional differential Zakharov-Kuznetsov equation to nonlinear partial differentia...

In this paper, a new heuristic scheme for the approximate solution of the generalized Burgers'-Fisher equation is proposed. The scheme is based on the hybridization of Exp-function method with nature inspired algorithm. The given nonlinear partial differential equation (NPDE) through substitution is converted into a nonlinear ordinary differential equation (NODE). The travelling wave solution i...

In this paper, we propose a new numerical algorithm, namely q-homotopy analysis Sumudu transform method (q-HASTM), to obtain the approximate solution for the nonlinear fractional dynamical model of interpersonal and romantic relationships. The suggested algorithm examines the dynamics of love affairs between couples. The q-HASTM is a creative combination of Sumudu transform technique, q-homotop...

The main objective of current study is investigation on thermo-hydraulic behavior nanofluids in a sinusoidal wavy channel as novel geometry under influences thermophoresis and Brownian motion. Differential quadrature method optimal homotopy asymptotic scheme have been employed to solve the momentum, continuity, energy nanoparticle fraction equations. validity proposed approaches evaluated by co...

In this paper we relate two topological invariants of a separable C*-algebras. The first is the shape invariant first studied by Effros and Kaminker [EK] and then developed further by Blackadar [B]. The second invariant is the isomorphism class of a C*-algebra in the asymptotic homotopy category A introduced by Connes and Higson [CH]. We prove that two separable C*-algebras are shape equivalent...

There are various applications where homotopy constraints are useful in trajectory generation for mobile robots. In this paper, we present a method to generate an optimal trajectory restricted to a particular homotopy class, which is specified by a given representative trajectory. The optimality is achieved by formulating the trajectory generation problem as a Mixed-Integer Quadratic Program (M...

in this paper, nonlinear klein-gordon equation with quadratic term is solved by means of an analytic technique, namely the homotopy analysis method (ham).comparisons are made between the adomian decomposition method (adm), the exact solution and homotopy analysis method. the results reveal that the proposed method is very effective and simple.