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...

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...

This paper has adopted rational approximation based on Regular Newton method, for frequency domain fitting of transfer functions of fractional order integrators (FOIs). Further, different discretized mathematical models of one-half, one-third and one-fourth order integrators based on Al-Alaoui operator and New optimized four segment operator have been also developed using these rational approxi...

fractional calculus has been used to model the physical and engineering processes that have found to be best described by fractional differential equations. for that reason, we need a reliable and efficient technique for the solution of fractional differential equations. the aim of this paper is to present an analytical approximation solution for linear and nonlinear multi-order fractional diff...