in this paper, we consider the second-kind chebyshev polynomials (skcps) for the numerical solution of the fractional optimal control problems (focps). firstly, an introduction of the fractional calculus and properties of the shifted skcps are given and then operational matrix of fractional integration is introduced. next, these properties are used together with the legendre-gauss quadrature fo...

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

In this paper, we study a new operational numerical method for hybrid fuzzy fractional differential equations by using of the hybrid functions under generalized Caputo- type fuzzy fractional derivative. Solving two examples of hybrid fuzzy fractional differential equations illustrate the method.

Analytical solution of thermo diffusion effect on magnetohydrodynamics flow fractionalized Cassonfluid over a vertical plate immersed in porous media is obtained. Moreover, the model problem, additional effects, like chemical reaction, heat source/sink, and thermal radiation are also considered.The solved by three approaches, namely, Atangana-Baleanu, Caputo-Fabrizio, Caputo fractionalderivativ...

‎in this paper‎, ‎we provide sufficient conditions for the existence of nonnegative solutions of a boundary value problem for a fractional order differential equation‎. ‎by applying kranoselskii`s fixed--point theorem in a cone‎, ‎first we prove the existence of solutions of an auxiliary bvp formulated by truncating the response function‎. ‎then the arzela--ascoli theorem is used to take $c^1$ ...

Introduction of fractional derivatives to the mechanics fluid flow is relatively new. Even though exact geometrical representations on have not been discovered, recent literatures proven that it a paradox will be useful in future. Meanwhile, Riga plates are actuators convenient for controlling velocity flows. Widely used field marine engineering, properties flowing over worth investigating. Thu...

the complex-step derivative approximation is applied to compute numerical derivatives. in this study, we propose a new formula of fractional complex-step method utilizing jumarie definition. based on this method, we illustrated an approximate analytic solution for the fractional cauchy-euler equations. application in image denoising is imposed by introducing a new fractional mask depending on s...

in this paper we introduce a type of fractional-order polynomials basedon the classical chebyshev polynomials of the second kind (fcss). also we construct the operationalmatrix 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.