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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]

We introduce the concept of an effective neutrosophic soft set, which aims to capture the influence on three independent membership functions representing degrees of truth (T), indeterminacy (I) and falsity (F). We go further by presenting a generalization of the effective neutrosophic soft set, which includes the incorporation of a degree to signify the potential for an approximate value-set. This enhancement contributes to improved efficiency and realism in the concept. Notably, this innovative approach leverages the strengths of both the generalized neutrosophic set and the effective neutrosophic soft set. The subsequent sections delve into fundamental operations on the generalized effective neutrosophic soft set, providing clarity through illustrative examples and propositions. Furthermore, we demonstrate the practical application of the generalized effective neutrosophic soft set in addressing decision-making problems and medical diagnoses. [ABSTRACT FROM AUTHOR]

This paper is a combination of time neutrosophic soft sets and Q- neutrosophic soft expert sets. We define the general concept of time Q-neutrosophic soft expert sets and study its properties. Some operations such as complement, union, and intersection are explored. Then a hypothetical application of this concept in the decision-making problem is given. [ABSTRACT FROM AUTHOR]

We establish the hybrid concept of complex bipolar- valued neutrosophic soft set (CBVNSS) as a hybrid model of bipolar neutrosophic soft set (BNSS)and complex fuzzy set (CFS). A CBVNSS is highly suitable for use in real life situations where the decision makers are interested to deal with bipolarity as well as truth membership, indeterminacy membership and falsity membership grades to the alternatives in an extended range with complex numbers. Certain operations on CBVNSS like complement, subset, union and intersection operations are defined. Some related examples are also given to enhance the understanding of the proposed concept. The basic properties are also verified. We then provide a decision-making method on the CBVNSS. Finally, a numerical example has been presented to verify validity and feasibility of the developed method. [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]