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Abstract: An algorithm has been developed to convert the multi-order fractional differential equation:where m < α ⩽ m +1, 0< β 1 < β 2 <⋯< β n < α and denotes Caputo fractional derivative of order α into a system of fractional differential equations. Further Adomian decomposition method has been employed to solve the system of fractional differential equations. Some illustrative examples are presented. [Copyright &y& Elsevier]

Abstract: In this paper, a new generalized Taylor’s formula of the kindwhere a j ∈ R , x > a, 0< α ⩽1, is established. Such an expression is precisely the classical Taylor’s formula in case of α =1. In addition, detailed expressions for and a j (α), that involving Caputo fractional derivatives, are well constructed. Some applications including approximation of functions and solutions of fractional differential equations are also given. [Copyright &y& Elsevier]

Abstract: In this paper, a new modification of the Adomian decomposition method is effectively implemented for solving fractional diffusion-wave equations that will facilitate the calculations, where the fractional derivative is based on Caputo definition. The proposed algorithm gives an analytical solution in the form of a convergent series with easily computable components. Numerical examples are given to show the application of the present algorithm. The new modification introduces a promising tool for many partial differential equations. [Copyright &y& Elsevier]

Abstract: The aim of the present analysis is to apply Adomian decomposition method for the solution of a nonlinear fractional differential equation. Finally, the solution obtained by the decomposition method has been numerically evaluated and presented in the form of tables and then compared with those obtained by truncated series method. A good agreement of the results is observed. [Copyright &y& Elsevier]