We study the equivalences and implications between linear (or homogeneous) nth order fractional differential equations (FDEs) integral in spaces L1(a,b) C[a,b] when n≥ 2. establish equivalence of IVP FDE subject to initial condition u(i)(a)=ui for i {0,1,...,n-1} n≥2. The difficulty is that known conditions such first FDEs are not sufficient with In this article we provide additional ensure par...

In this paper, we focus on the study of implicit FDE involving Stieltjes integral boundary conditions. We first exploit some sufficient conditions to guarantee existence and uniqueness solutions for above problems based Banach contraction principle Schaefer’s fixed point theorem. Then, present different kinds stability such as UHS, GUHS, UHRS, GUHRS by employing classical techniques. end, main ...

In recent years, many works on the subject of fractional calculus contain interesting accounts of the theory and applications of fractional calculus operators in a number of areas of mathematical analysis ( such as ordinary and partial differential equations, integral equations, summation of series, etc.). The main object of this paper is to construct multivariable extension of Jacobi polynomia...

High-order adaptive methods for fractional differential equations are proposed. The methods rely on a kernel reduction method for the approximation and localization of the history term. To avoid complications typical to multistep methods, we focus our study on 1-step methods and approximate the local part of the fractional integral by integral deferred correction to enable high order accuracy. ...

In this paper, the multiple solutions of Nth-order fuzzy differential equations by the equivalent integral forms are considered. Also, an Existence and uniqueness theorem of solution of Nth-order fuzzy differential equations is proved under Nth-order generalized differentiability in Banach space.

In the paper we consider fuzzy stochastic integral equations using the methods of stochastic inclusions. The idea is to consider an associated martingale problem and its solutions in order to obtain a solution to the fuzzy stochastic equation.