Cauchy Problem for Differential Equation with Caputo Derivative

The paper is devoted to the study of the Cauchy problem for a nonlinear\ndifferential equation of complex order with the Caputo fractional derivative.\nThe equivalence of this problem and a nonlinear Volterra integral equation\nin the space of continuously differentiable functions is established. On the\nbasis of this result, the existence and uniqueness of the solution of the\nconsidered Cauchy problem is proved. The approximate-iterative method\nby Dzjadyk is used to obtain the approximate solution of this problem. Two\nnumerical examples are given.

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