In this paper, homotopy analysis method is presented for linear system of first-order fuzzy differential equations which involves a radioactivity decay model. We give the illustrative example to demonstrate the efficiency of the method. Finally, homotopy analysis method (HAM) is applied to obtain series solutions to the the radioactivity decay model.

The convergence of qhomotopy analysis method (q-HAM) is studied in the present paper. It is proven that under certain conditions the solution of the equation: 1 ∅ , ∅ , 0 associated with the original problem exists as a power series in .So,under a special constraint the q-homotopy analysis method does converge to the exact solution of nonlinear problems. An error estimate is also provided. The ...

From a spectral method combined with a predictor-corrector scheme, we numerically study the behavior in time of solutions of the three-dimensional generalized Kadomtsev-Petviashvili equations regularized using the BBM trick. The solution no longer blows up and the solitonic behavior is observed.

The work  addressed in this paper is a comparative study between convergence of the  acceleration techniques, diagonal pad'{e} approximants and shanks transforms, on Homotopy analysis method  and Adomian decomposition method for solving  differential equations of integer and fractional orders.

The maximum principle for the space and time-space fractional partial differential equations is still an open problem. In this paper, we consider a multi-term time-space Riesz-Caputo fractional differential equations over an open bounded domain. A maximum principle for the equation is proved. The uniqueness and continuous dependence of the solution are derived. Using a fractional predictor-corr...

In this paper, we prove the convergence of homotopy analysis method (HAM). We also apply the homotopy analysis method to obtain approximate analytical solutions of systems of the second kind Volterra integral equations. The HAM solutions contain an auxiliary parameter which provides a convenient way of controlling the convergence region of series solutions. It is shown that the solutions obtain...

The homotopy analysis method HAM is employed to obtain symbolic approximate solutions for nonlinear coupled equations with parameters derivative. These nonlinear coupled equations with parameters derivative contain many important mathematical physics equations and reaction diffusion equations. By choosing different values of the parameters in general formal numerical solutions, as a result, a v...

Here, an analytic technique, namely the homotopy analysis method (HAM), is applied to solve a generalized Hirota–Satsuma coupled KdV equation. HAM is a strong and easy-to-use analytic tool for nonlinear problems and dose not need small parameters in the equations. Comparison of the results with those of Adomian’s decomposition method (ADM) and homotopy perturbation method (HPM), has led us to s...