HADAMARD FRACTIONAL CALCULUS ON TIME SCALES

This study defines a Hadamard fractional sum by use of the time-scale theory. Then a h-fractional difference is given and fundamental theorems are proved. Initial value problems of fractional difference equations are presented and their equivalent fractional sum equations are provided. The discrete Mittag-Leffler function solutions of linear fractional difference equations are obtained. It can be concluded that the new discrete fractional calculus of Hadamard type is well defined.

Automated summary

This study introduces a Hadamard fractional sum based on the time-scale theory and defines h-fractional difference. It proves fundamental theorems and presents initial value problems of fractional difference equations, providing their equivalent fractional sum equations. It also derives the discrete Mittag-Leffler function solutions for linear fractional difference equations. The study concludes that the new discrete fractional calculus of Hadamard type is well defined.