In this paper we introduce a type of fractional-order polynomials based on the classical Chebyshev polynomials of the second kind (FCSs). Also we construct the operational matrix of fractional derivative of order $ gamma $ in the Caputo for FCSs and show that this matrix with the Tau method are utilized to reduce the solution of some fractional-order differential equations.

The aim of this paper is to establish the existence of solutions of boundary value problems of nonlinear fractional integro-differential equations involving Caputo fractional derivative by using the techniques such as fractional calculus, H"{o}lder inequality, Krasnoselskii's fixed point theorem and nonlinear alternative of Leray-Schauder type. Examples are exhibited to illustrate the main resu...

Abstract In this article, the main objective is to establish Grüss-type fractional integral inequalities by employing Caputo-Fabrizio integral.

and Applied Analysis 3 Let Γ(⋅) denote the gamma function. For any positive integer n and real number θ (n − 1 < θ < n), there are different definitions of fractional derivatives with order θ in [8]. During this paper, we consider the left, (right) Caputo derivative and left (right) Riemann-Liouville derivative defined as follows: (i) the left Caputo derivative: C 0 D θ t V (t) = 1 Γ (n − θ) ∫ ...

We correct a recent result concerning the fractional derivative at extreme points. We then establish new results for the Caputo and Riemann-Liouville fractional derivatives at extreme points.

In this paper, the fractional Sturm-Liouville problems, in which the second order derivative is replaced by a fractional derivative, are derived by the Homotopy perturbation method. The fractional derivatives are described in the Caputo sense. The present results can be implemented on the numerical solutions of the fractional diffusion-wave equations. Numerical results show that HPM is effectiv...

This paper investigates the magnetic blood flow in an inclined multi-stenosed artery under influence of a uniformly distributed field and oscillating pressure gradient. The is modelled using non-Newtonian Casson fluid model. governing fractional differential equations are expressed by Caputo-Fabrizio derivative without singular kernel. Exact analytical solutions obtained Laplace finite Hankel t...

In this article, a generalized midpoint-type Hermite–Hadamard inequality and Pachpatte-type via new fractional integral operator associated with the Caputo–Fabrizio derivative are presented. Furthermore, identity for differentiable convex functions of first order is proved. Then, taking into account as an auxiliary result assistance Hölder, power-mean, Young, Jensen inequality, some estimations...