in this paper, we introduce a family of fractional-order chebyshev functions based on the classical chebyshev polynomials. we calculate and derive the operational matrix of derivative of fractional order $gamma$ in the caputo sense using the fractional-order chebyshev functions. this matrix yields to low computational cost of numerical solution of fractional order differential equations to the ...

In this paper, we obtain new Lyapunov-type inequalities for the third-order linear differential equation x′′′ + q(t)x = 0 . Our work provides the sharpest results in the literature and makes corrections to those in a recently published paper [1]. Based on the above, we further establish new Lyapunov-type inequalities for more general third-order linear differential equations. Moreover, by combi...