A Novel Approach to Solving Fractional-Order Kolmogorov and Rosenau–Hyman Models through the q-Homotopy Analysis Transform Method

Solving The Optimal Control Problems Using Homotopy Perturbation Transform Method

Inthispaper,wesolveHamilton-Jocobi-Bellman(HJB)equationsarisinginoptimalcontrolproblems usingHomotopyPerturbationTransformMethod(HPTM).Theproposedmethodisacombinedform oftheLaplaceTransformationMethodwiththeHomotopyPerturbationMethodtoproduceahighly effectivemethodtohandlemanyproblems. ApplyingtheHPTM,solutionprocedurebecomeseasier, simplerandmorestraightforward. Someillustrativeexamplesaregive...

Homotopy Perturbation Method for Solving Strum-Liouville Problms of Fractional Order

Solving Fractional Fornberg-whitham Equation by Homotopy Analysis Method

In this paper, The analytical solution of the nonlinear Fornberg-Whitham equation with fractional time derivative was derived by means of the homotopy analysis method. The fractional derivatives are described in the Caputo sense. By choosing different values of the parameters in general formal numerical solutions, as a result, a very rapidly convergent series solution is obtained. The results r...

Homotopy Analysis Method for Solving Fractional Diffusion Equation

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...

Solving Fuzzy Impulsive Fractional Differential Equations by Homotopy Perturbation Method

In this paper, we study semi-analytical methods entitled Homotopy pertourbation method (HPM) to solve fuzzy impulsive fractional differential equations based on the concept of generalized Hukuhara differentiability. At the end first of Homotopy pertourbation method is defined and its properties are considered completely. Then econvergence theorem for the solution are proved and we will show tha...