Abstract:
In this thesis, we present the resolvent kernal method and the Legendre approximation method to
obtain the numerical solution of fractional differential equations. For this purpose, we convert the
fractional differential equation to a fractional integral equation. The solution of the equivalent
fractional integral equation is derived by the resolvent kernal method. When the exact fractional
integration of the forcing function in differential equations is not possible, we approximate it by
fractional Legendre polynomials. We obtained the numerical solution to the Darboux problem
by using the resolvent kernal method. The convergence of the resolvent kernal method is also
provided. Furthermore, we presented a Legendre approximation method for the numerical solution
of the Darboux problem. Every method is accompanied by a numerical example to verify the
applicability and effectiveness of the proposed methods.
