This paper deals with some existence, uniqueness and Ulam-Hyers-Rassias stability results for a class of implicit fractional q-difference equations. Some applications are made of some fixed point theorems in Banach spaces for the existence and uniqueness of solutions, next we prove that our problem is generalized Ulam-Hyers-Rassias stable. Two illustrative examples are given in the last section.

This paper deals with some existence and Ulam stability results for some classes of implicit fractional q-difference equations with and without random effects in Banach spaces and Banach algebras. Our results are provided by applying the fixed point theory (Itoh's random fixed point theorem, the nonlinear alternative of Schaefer's type proved by Dhage, and an other Dhage's random fixed point theorem in Banach algebras). Other results about the extremal solutions and random extremal solutions under Carathéodory and certain monotonicity conditions are proved. In the final section, some illustrative examples are provided.

No abstract

This article deals with some results about the existence of solutions and bounded solutions and the attractivity for a class of fractional q-difference equations. Some applications are made of Schauder fixed point theorem in Banach spaces and Darbo fixed point theorem in Fréchet spaces. We use some technics associated with the concept of measure of noncompactness and the diagonalization process. Some illustrative examples are given in the last section.

"This paper deals with some existence results for a class of implicit fractional q-difference equations. The results are based on the fi xed point theory in Banach spaces and the concept of measure of noncompactness. An illustrative example is given in the last section."