Ulam-Hyers stability results for a novel nonlinear Nabla Caputo fractional variable-order difference system
Danfeng Luo, Thabet Abdeljawad, Zhiguo Luo
Abstract
This paper is concerned with a kind of nonlinear Nabla Caputo fractional difference system with variable-order and fixed initial valuable. By applying Krasnoselskii's fixed point theorem, we give some sufficient conditions to guarantee the existence results for the considered fractional discrete equations. In addition, we further consider the Ulam-Hyers stability by means of generalized Gronwall inequality. At last, two typical examples are delineated to demonstrate the effectiveness of our theoretical results.
Topics & Concepts
MathematicsNabla symbolNonlinear systemFixed-point theoremStability (learning theory)Variable (mathematics)Order (exchange)Applied mathematicsGronwall's inequalityFractional calculusMathematical analysisInequalityQuantum mechanicsFinanceComputer sciencePhysicsMachine learningEconomicsOmegaFractional Differential Equations SolutionsNonlinear Differential Equations AnalysisMathematical and Theoretical Epidemiology and Ecology Models