$C^{3}$-spline Methods for Solving Fractional Integro-differential Equations

Fractional integro-differential equations (FIDEs) constitute an important mathematical tool in modeling many dynamical processes‎. ‎To solve FIDEs‎, ‎several analytical and numerical methods have been proposed‎, ‎namely those based on symmetry and spline approaches‎. ‎This paper proposes quartic and sextic $C^{3}$-spline methods for the numerical solution of FIDEs‎. ‎The convergence analysis of the proposed strategy is examined in detail‎. ‎Finally‎, ‎three numerical examples are given to illustrate the numerical accuracy and efficiency of the proposed strategy‎.