Some Results on the q-Calculus and Fractional q-Differential Equations
Ying Sheng, Tie Zhang
Abstract
In this paper, we first discuss some important properties of fractional q-calculus. Then, based on these properties and the q-Laplace transform, we translate a class of fractional q-differential equations into the equivalent q-differential equations with integer order. Thus, we propose a method for solving some linear fractional q-differential equations by means of solving the corresponding integer order equations. Several examples are provided to illustrate our solution method.
Topics & Concepts
Laplace transformFractional calculusMathematicsInteger (computer science)Differential equationTime-scale calculusOrder (exchange)Class (philosophy)Applied mathematicsMathematical analysisCalculus (dental)Multivariable calculusComputer scienceProgramming languageArtificial intelligenceFinanceEngineeringMedicineControl engineeringDentistryEconomicsFractional Differential Equations SolutionsMathematical functions and polynomialsAdvanced Mathematical Identities