Differential Equation of Fractional Order Caputo Derivative Existence and Uniqueness Theorem Approximate-Iterative Method 34A12 34B15 26A33 65L10
Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Fractional Calculus and Applied Analysis, Vol. 7, No 3, (2004), 297p-321p
The paper is devoted to the study of the Cauchy problem for a nonlinear
differential equation of complex order with the Caputo fractional derivative.
The equivalence of this problem and a nonlinear Volterra integral equation
in the space of continuously differentiable functions is established. On the
basis of this result, the existence and uniqueness of the solution of the
considered Cauchy problem is proved. The approximate-iterative method
by Dzjadyk is used to obtain the approximate solution of this problem. Two
numerical examples are given.