ABSTRACT
Let X be a Banach space and T be a bounded linear operator defined on X. In this work we study the existence of solutions of a class of nonlinear difference equation of fractional order in the form where corresponds to the fractional difference operator of order in sense of Riemann–Liouville and is a function satisfying suitable conditions. More specifically, by using operator-theoretical methods and fixed point theory, we show the existence of solutions of such class of equations on the vector-valued weighted space of sequences
2010 AMS MATHEMATICS SUBJECT CLASSIFICATIONS:
Disclosure statement
No potential conflict of interest was reported by the author.