in this paper we apply hybrid functions of general block-pulse‎ ‎functions and legendre polynomials for solving linear and‎ ‎nonlinear multi-order fractional differential equations (fdes)‎. ‎our approach is based on incorporating operational matrices of‎ ‎fdes with hybrid functions that reduces the fdes problems to‎ ‎the solution of algebraic systems‎. ‎error estimate that verifies a‎ ‎converge...

In this study, an effective numerical method for solving fractional differential equations using Chebyshev cardinal functions is presented. The fractional derivative is described in the Caputo sense. An operational matrix of fractional order integration is derived and is utilized to reduce the fractional differential equations to system of algebraic equations. In addition, illustrative examples...

The study of the stability of differential equations without its explicit solution is of particular importance. There are different definitions concerning the stability of the differential equations system, here we will use the definition of the concept of Lyapunov. In this paper, first we investigate stability analysis of distributed order fractional differential equations by using the asympto...

This paper is concerned with the state estimation problem in nonlinear fractional order discrete state-space systems with uncertain observations, when the random interruptions in the observation process are modelled by independent Bernoulli random variables. Two filtering algorithms are proposed for this class of systems; the first one is a generalization of the extended fractional Kalman filte...

The Arakawa-Kaneko zeta functions interpolate the poly-Bernoulli numbers at the negative integers and their values at positive integers are connected to multiple zeta values. We give everywhere-convergent series expansions of these functions in terms of Bernoulli polynomials and Dirichlet series related to harmonic numbers, exhibiting their explicit analytic continuation. Differentiating the Ba...

in this paper, a technique generally known as meshless numerical scheme for solving fractional dierential equations isconsidered. we approximate the exact solution by use of radial basis function(rbf) collocation method. this techniqueplays an important role to reduce a fractional dierential equation to a system of equations. the numerical results demonstrate the accuracy and ability of this me...