Fractional q-Difference Equations

Abstract

AbstractAs in the classical theory of ordinary fractional differential equations, q-difference equations of fractional order are divided into linear, nonlinear, homogeneous, and inhomogeneous equations with constant and variable coefficients. This chapter is devoted to certain problems of fractional q-difference equations based on the basic Riemann–Liouville fractional derivative and the basic Caputo fractional derivative. In this chapter, we investigate questions concerning the solvability of these equations in a certain space of functions. A special class of Cauchy type q-fractional problems is also developed at the end of this chapter.KeywordsFractional Ordinary Differential EquationsFractional DerivativeFractional-order SystemsRiemann LiouvilleCauchy Type ProblemThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.