# Solving linear fractional order differential equations by Chebyshev polynomials based numerical inverse Laplace transform

### Abstract

Numerical inverse Laplace transform is employed in solving some fractional order differential equations that convert the linear fractional differential equations into the linear system of algebraic equations. The unknown function or the solution of fractional differential equations can be expressed in a series of orthogonal polynomials; Chebyshev polynomials of the second kind are so developed using odd cosine series. The efficacy of the technique is well tested on the initial value problem of fractional order differential equations, fractional oscillation equation and system of fractional-algebraic equations. We have also calculated the $L_{\infty}$-errors of obtained results which shows that the proposed method produces satisfactory results.