We suggest and analyze a technique by combining the variational iteration method and the homotopy perturbation method. This method is called the variational homotopy perturbation method. We use this method for solving Generalized Time-space Fractional Schrödinger equation. The fractional derivative is described in Caputo sense. The proposed scheme finds the solution without any discritization, ...

In this paper, the fractional Sturm-Liouville problems, in which the second order derivative is replaced by a fractional derivative, are derived by the Homotopy perturbation method. The fractional derivatives are described in the Caputo sense. The present results can be implemented on the numerical solutions of the fractional diffusion-wave equations. Numerical results show that HPM is effectiv...

In this letter, the powerful, easy-to-use and effective mathematical tool like Homotopy Analysis Method is used to solve the diffusion equation with fractional time derivative ) 1 0 (    . Using the initial condition, the approximate analytical solution of the problem is obtained. Choosing proper values of auxiliary and homotopy parameters, the convergence of the approximate series solution...

This paper examines the solution of a damped beam equation whose damping characteristics are well-defined by the fractional derivative (FD). Homotopy Analysis Method (HAM) is applied for calculating the dynamic response (DR). Unit step and unit impulse functions are deliberated for this analysis. Acquired results are illustrated to show the movement of the beam under various sets of parameters ...

A 2-D fractal heat conduction in a space is considered by He?s derivative. The two-scale transform adopted to convert the model its differential partner. homotopy perturbation method used find approximate analytical solution.

We have used the homotopy analysis method (HAM) to obtain solution of Davey-Stewartson equations of fractional order. The fractional derivative is described in the Caputo sense. The results obtained by this method have been compared with the exact solutions. Stability and convergence of the proposed approach is investigated. The effects of fractional derivatives for the systems under considerat...

In this paper, we applied the homotopy analysis method (HAM) to construct the analytical solutions of the space fractional diffusion equations. The derivatives are defined in the Jumarie’s fractional derivative sense. The explicit solutions of the equations have been presented in the closed form by using initial conditions. Two typical examples have been discussed. The results reveal that the m...

In this study, we present a new general solution to rational epidemiological mathematical model via recent intelligent method called the natural transform homotopy analysis (NTHAM), which combines two methods: (NTM) and (HAM). To assess precision reliability of method, compared obtained results with those Laplace perturbation (LHPM) as well q-homotopy Sumudu (q-HASTM), revealed that NTHAM is mo...

We develop two topics in parallel and show their inter-relation. The first centers on the notion of a fractional-differentiable structure on a commutative or a non-commutative space. We call this study quantum harmonic analysis. The second concerns homotopy invariants for these spaces and is an aspect of non-commutative geometry. We study an algebra A, which will be a Banach algebra with unit, ...