Fractional \(q\)-difference equations on the half line. (English) Zbl 1538.39007
Summary: 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.
MSC:
| 39A13 | Difference equations, scaling (\(q\)-differences) |
| 26A33 | Fractional derivatives and integrals |
Keywords:
fractional \(q\)-difference equation; attractivity; diagonalization; bounded solution; Banach space; Fréchet space; fixed pointReferences:
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