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In this work, we suggest a new numerical scheme called the fractional higher order Taylor method (FHOTM) to solve fractional differential equations (FDEs). Using the generalized Taylor's theorem is the fundamental concept of this approach. Then, the local truncation error generated by the suggested FHOTM is estimated by proving suitable theoretical results. At last, several numerical applications are given to demonstrate the applicability of the suggested approach in relation to their exact solutions. [ABSTRACT FROM AUTHOR]

This paper aims to propose a numerical approach to deal with systems of fractional stochastic differential equations. This approach, which is regarded as a modification of the fractional Euler method (FEM), is called the modified fractional Euler method (MFEM). A susceptible infected recovered model (SIR model) is taken into consideration as an example of a system of fractional stochastic differential equations. Such a model is solved with the use of the MFEM in its deterministic and stochastic cases for the purpose of comparing the fulfilled results. [ABSTRACT FROM AUTHOR]

This paper aims first to recall the generalized Mittag-Leffler function and propose several properties of the generalized matrix Mittag-Leffler function. Afterward, we set a definition for a further extension of the generalized matrix Mittag-Leffler function and then show that this function is absolutely convergent under a certain condition. [ABSTRACT FROM AUTHOR]