in this article we implement an operational matrix of fractional integration for legendre polynomials. we proposed an algorithm to obtain an approximation solution for fractional differential equations, described in riemann-liouville sense, based on shifted legendre polynomials. this method was applied to solve linear multi-order fractional differential equation with initial conditions, and the...

This paper proposes a new computational scheme for approximating variable-order fractional integral operators by means of finite element scheme. This strategy is extended to approximate the solution of a class of variable-order fractional nonlinear systems with time-delay. Numerical simulations are analyzed in the perspective of the mean absolute error and experimental convergence order. To ill...

in this article, we apply two new fixed point theorems to investigate the existence of mild solutions for a nonlocal fractional cauchy problem with an integral initial condition in banach spaces.

abstract. in this paper, we implement numerical solution of differential equations of frac- tional order based on hybrid functions consisting of block-pulse function and rationalized haar functions. for this purpose, the properties of hybrid of rationalized haar functions are presented. in addition, the operational matrix of the fractional integration is obtained and is utilized to convert compu...

Fractional differential equations and fractional integral equations have gained considerable importance and attention due to their applications in many engineering and scientific disciplines. Gronwall-Bellman inequalities are important tools in the study of existence, uniqueness, boundedness, stability and other qualitative properties of solutions of Fractional differential equations and fracti...

In this paper, we study the fuzzy Ulam-Hyers-Rassias stability for two kinds of fuzzy fractional integral equations by employing the fixed point technique.

In recent years, a remarkably large number of inequalities involving the fractional q-integral operators have been investigated in the literature by many authors. Here, we aim to present some new fractional integral inequalities involving generalized Erdélyi-Kober fractional q-integral operator due to Gaulué, whose special cases are shown to yield corresponding inequalities associated with Kobe...

In this article, we study the existence of integral solutions for two classes of fractional order evolution equations with nondensely defined linear operators. First, we consider the nonhomogeneous fractional order evolution equation and obtain its integral solution by Laplace transform and probability density function. Subsequently, based on the form of integral solution for nonhomogeneous fra...