RIGHT HADAMARD FRACTIONAL DIFFERENCES AND SUMMATION BY PARTS

Abstract

We investigate the right Hadamard fractional differences. First, a $Q$-operator is defined for continuous Hadamard fractional calculus. It shows that the left and right Hadamard operators satisfy a dual identity. Then, the $Q$-operator is extended to define the right Hadamard fractional sum and difference and present their properties. A terminal value problem is discussed by use of the right fractional difference. Finally, the related summation by parts formulas are obtained. It can be concluded that the right Hadamard fractional sum and difference are well defined.