A novel solution procedure for fuzzy fractional heat equations by homotopy analysis transform method

On Fuzzy Fractional Laplace Transformation

“…In Figures 5, 6, 7, and 8 we have sketched the solutions for the case of fractional, fractional fuzzy, and fuzzy, respectively. Applying Laplace transform and inverse Laplace transform on (27) one is led to Therefore, the general solution will be as follows: And the general solution will be as = ( ( , ) , ( , )) . Figures 17, 18, 19, and 20 present the graphs of the solutions for the cases of fractional, fuzzy fractional, and fuzzy, respectively.…”

“…As a consequence, there is vast literature on the practical applications of fuzzy sets, while theory has a more modest coverage. Fuzzy fractional heat and wave equation has been solved by using homotopy analysis transform method [27]. This paper adopted fuzzy Laplace transforms method to solve problems of fuzzy fractional differential equations.…”

A New Efficient Method for Solving Two-Dimensional Nonlinear System of Burger’s Differential Equations

“…Additionally, like this, it also appears in varied areas of applied mathematics and physics, such as modelling of gas dynamics [1][2][3][4][5]. Recently, many numerical and analytical methods have been used to study the two-dimensional Burger's equation such as the differential transformation method [6], homotopy perturbation method [7], homotopy analysis method [8], variational iteration method [9], Adomian decomposition method [10][11][12], cubic B-spline differential quadrature method [13], finite difference method [14], finite element [15], and local discontinuous Galerkin finite element method [16] and also mathematicians have used transform methods coupled with analytical methods [17][18][19][20][21][22][23][24][25][26][27][28][29][30] to solve PDEs. e Sumudu decomposition method (SDM) is one of these methods, and it has been successfully used to solve intricate problems in engineering mathematics and applied science [31][32][33][34][35].…”

Comparison of optimal homotopy analysis method and fractional homotopy analysis transform method for the dynamical analysis of fractional order optical solitons

“…35 The important feature of FHATM is that two effective methods are used in harmony to obtain the series solution of partial differential equations with swift convergence. 36,37 In this article, after summarizing the current challenges and solutions to the integer and fractional order optical wave problems, we have compared the two semi-analytic techniques and have presented the approximate results. Our analysis shows that the NLSE can be best solved by the OHAM by controlling the order of accuracy.…”