In this paper, a sufficient condition for stability of a system of nonlinear multi-fractional order differential equations on a finite time interval with an illustrative example, has been presented to demonstrate our result. Also, an idea to extend our result on such system on an infinite time interval is suggested.

            In this paper, several conditions are put in order to compose the sequence of partial sums ,  and  of the fractional operators of analytic univalent functions ,  and   of bounded turning which are bounded turning too.

In this paper, the computational method (CM) based on the standard polynomials has been implemented to solve some nonlinear differential equations arising in engineering and applied sciences. Moreover, novel computational methods have been developed in this study by orthogonal base functions, namely Hermite, Legendre, and Bernstein polynomials. The nonlinear problem is successfully converted into a nonlinear algebraic system of equations, which are then solved by Mathematica^®12. The developed computational methods (D-CMs) have been applied to solve three applications involving well-known nonlinear problems: the Darcy-Brinkman-Forchheimer equation, the Blasius equation, and the Falkner-Skan equation, and a comparison between t

In this research article, an Iterative Decomposition Method is applied to approximate linear and non-linear fractional delay differential equation. The method was used to express the solution of a Fractional delay differential equation in the form of a convergent series of infinite terms which can be effortlessly computable.
The method requires neither discretization nor linearization. Solutions obtained for some test problems using the proposed method were compared with those obtained from some methods and the exact solutions. The outcomes showed the proposed approach is more efficient and correct.

 In this paper, we introduce and discuss an algorithm for the numerical solution of two- dimensional fractional partial differential equation with parameter. The algorithm for the numerical solution of this equation is based on implicit and an explicit difference method. Finally, numerical example is provided to illustrate that the numerical method for solving this equation is an effective solution method.

In this paper, we will study and prove the existence and the uniqueness theorems
of solutions of the generalized linear integro-differential equations with unequal
fractional order of differentiation and integration by using Schauder fixed point
theorem. This type of fractional integro-differential equation may be considered as a
generalization to the other types of fractional integro-differential equations
Considered by other researchers, as well as, to the usual integro-differential
equations.

Recently, the financial mathematics has been emerged to interpret and predict the underlying mechanism that generates an incident of concern. A system of differential equations can reveal a dynamical development of financial mechanism across time. Multivariate wiener process represents the stochastic term in a system of stochastic differential equations (SDE). The standard wiener process follows a Markov chain, and hence it is a martingale (kind of Markov chain), which is a good integrator. Though, the fractional Wiener process does not follow a Markov chain, hence it is not a good integrator. This problem will produce an Arbitrage (non-equilibrium in the market) in the predicted series. It is undesired property that leads to erroneous conc

In This paper generalized spline method and Caputo differential operator is applied to solve linear fractional integro-differential equations of the second kind. Comparison of the applied method with exact solutions reveals that the method is tremendously effective.