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Cauchy Problem for Differential Equation with Caputo Derivative

Kilbas, Anatoly, Marzan, Sergei (2004)

Fractional Calculus and Applied Analysis

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...

Cauchy problem with Denjoy-Stieltjes integral

María Guadalupe Morales Macías (2024)

Mathematica Bohemica

This work is devoted to analyzing the existence of the Cauchy fractional-type problems considering the Riemann-Liouville derivative (in the distributional Denjoy integral sense) of real order n 1 . These kinds of equations are a generalization of the measure differential equations. Our results extend A. A. Kilbas, H. M. Srivastava, J. J. Trujillo (2006) and H. Zhou, G. Ye, W. Liu, O. Wang (2015).

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