Cauchy problem with Denjoy-Stieltjes integral

Abstract

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 $n\geq1$. 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).

Keywords

• fractional measure differential equation
• cauchy problem
• riemann-liouville fractional integral and derivative
• distributional denjoy integral