in this paper, we apply the  homotopy analysis method (ham) for solving fuzzy  linear systems and present  the necessary and sufficient conditions for the convergence of series solution obtained via the ham. also, we present a new criterion for choosing a proper value of convergence-control parameter $hbar$ when the ham is applied to linear system of equations. comparisons are made between the ...

In this paper, we present an efficient numerical algorithm, namely block homotopy perturbation method, for solving fuzzy linear systems based on homotopy perturbation method. Some numerical examples are given to show the efficiency of the algorithm. Keywords—Homotopy perturbation method, Fuzzy linear systems, Block linear system, Fuzzy solution, Embedding parameter.

In this paper, we apply the homotopy perturbation method for solving the sixth-order boundary value problems by reformulating them as an equivalent system of integral equations. This equivalent formulation is obtained by using a suitable transformation. The analytical results of the integral equations have been obtained in terms of convergent series with easily computable components. Several ex...

In this paper, an efficient modification of homotopy perturbation method, namely optimal homotopy perturbation method, is introduced for solving linear and nonlinear partial differential equations with large solution domain based on a new homotopy perturbation method and Padé approximation method. We compare the performance of the method with those of new homotopy perturbation and optimal varia...

in this paper, we apply the local fractional laplace transform method (or yang-laplace transform) on volterra integro-differential equations of the second kind within the local fractional integral operators to obtain the analytical approximate solutions. the iteration procedure is based on local fractional derivative operators. this approach provides us with a convenient way to find a solution ...

In the finance market, Black–Scholes equation is used to model price change of underlying fractal transmission system. Moreover, fractional differential equations recently are accepted by researchers that a powerful tool in studying geometry and dynamics. Fractional modeling various important situations or phenomena real world such as fluid flow, acoustics, electromagnetic, electrochemistry mat...

In this paper, we present a comparative analysis of non-reactive contaminant flow problem for constant initial concentration in two dimensions by homotopy-perturbation and Variational Iteration method. We provide an approximation of this equation using homotopy-perturbation transformation and solve the resulting linear equations analytically by homotopy-perturbation method (HPM) and Variational...

In this paper, we will study about Fractional-order partial differential equations in Mathematical Science and introduce analyse fractional calculus with an integral operator that contains the Caputo- Fabrizio’s fractional-order derivative. The advanced method is appropriate union of new transform named as ‘Mohand transform’ homotopy perturbation method. Some numerical examples are used to comm...