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 deals with the application of fourth kind Chebyshev wavelets (FKCW) in solving numerically a model of HIV infection of CD4+T cells involving Caputo fractional derivative. The present problem is a system of nonlinear fractional differential equations. The goal is to approximate the solution in the form of FKCW truncated series. To do this, an operational matrix of fractional integrati...

We analyze the asymptotic rates of convergence of Chebyshev, Legendre and Jacobi polynomials. One complication is that there are many reasonable measures of optimality as enumerated here. Another is that there are at least three exceptions to the general principle that Chebyshev polynomials give the fastest rate of convergence from the larger family of Jacobi polynomials. When f (x) is singular...

Integral inequalities are very important in applied sciences. Chebyshev's integral inequality is widely used mathematics. First of all, some necessary definitions and results regarding conformable derivative given this article. Then we give Chebyshev for simultaneously positive (or negative) functions using the fractional derivative. We Gronwall to prove our results, unlike other studies litera...

In this paper, we tried to evaluate the fractional derivatives by using the Chebyshev series expansion. We discuss the indefinite quadrature rule to estimate the fractional derivatives of Riemann-Liouville type.

The main objective of this paper is to use the generalized proportional Hadamard fractional integral operator establish some new inequalities for extended Chebyshev functionals. In addition, we investigate positive continuous functions by employing a operator. findings study are theoretical but have potential help solve additional practical problems in mathematical physics, statistics, and appr...

The design of fractional order inverse Chebyshev low pass filter has been presented in this paper. (1+α) filters have designed by comparing the transfer function notch with second-order filter. Particle swarm optimization utilized to derive coefficients fractional-order varying α from 0.1 0.9. canonical forms these realized using multiple input Biquad circuits. value circuit elements for each d...