On new updated concept for delay differential equations with piecewise Caputo fractional-order derivative
Khursheed J. Ansari, Asma Asma, Fatima Ilyas, Kamal Shah, Aziz Khan, Thabet Abdeljawad
Abstract
This study introduces some updated results for piecewise mixed delay equations with Caputo-type fractional-order derivatives. We establish some necessary results for the aforementioned problem devoted to the existence and uniqueness of the solution and different forms of Ulam Hyers (U-H) type stability. To obtain the required results, fixed point theorems described by Krasnoselskii and Banach are used. Furthermore, the results related to U-H stabilities are determined by using the basic concept of nonlinear analysis. To illustrate our results, we provide a relevant test problem.
Topics & Concepts
MathematicsUniquenessPiecewiseFractional calculusFixed-point theoremStability (learning theory)Order (exchange)Type (biology)Applied mathematicsNonlinear systemDerivative (finance)Differential equationMathematical analysisComputer scienceMachine learningQuantum mechanicsEcologyPhysicsFinancial economicsBiologyEconomicsFinanceFractional Differential Equations SolutionsNonlinear Differential Equations AnalysisNumerical methods for differential equations