On the Stability of Incommensurate h-Nabla Fractional-Order Difference Systems
Noureddine Djenina, Adel Ouannas, Taki-Eddine Oussaeif, Giuseppe Grassi, Iqbal M. Batiha, Shaher Momani, Ramzi B. Albadarneh
Abstract
This work aims to present a study on the stability analysis of linear and nonlinear incommensurate h-nabla fractional-order difference systems. Several theoretical results are inferred with the help of using some theoretical schemes, such as the Z-transform method, Cauchy–Hadamard theorem, Taylor development approach, final-value theorem and Banach fixed point theorem. These results are verified numerically via two illustrative numerical examples that show the stabilities of the solutions of systems at hand.
Topics & Concepts
Nabla symbolHadamard transformMathematicsOrder (exchange)Stability (learning theory)Nonlinear systemFixed-point theoremApplied mathematicsCauchy distributionWork (physics)Pure mathematicsCauchy problemMathematical analysisInitial value problemPhysicsComputer scienceQuantum mechanicsOmegaFinanceEconomicsMachine learningFractional Differential Equations SolutionsAdvanced Control Systems DesignNonlinear Differential Equations Analysis