On System of Volterra Integro-Fractional Differential Equations : Theorems, Analytic and Approximate Methods, Existence and Uniqueness of a Solution

In chapter one, some new formulas for Caputo fractional derivatives of some elementary functions is given. The system of M-linear Voltera integro-fractional differential equations is reduced into a system of Voltera integral equations and the global and semi-global fundamental existence and uniquenas theorems and presented in Chapter two. In chapter three, some analytic and approximate methods are applied to treat such a system. In chapter four, Runge-Kutta methods with different orders are given to treat such a system. The convergence and stability are also investigated. In chapter five, special Chebyshev method is considered. In chapter six, conclusions and recommendations with comparisons between the methods are included.