On continuity of the fractional derivative of the time-fractional semilinear pseudo-parabolic systems
Erdal Karapınar, Ho Duy Binh, Nguyen Hoang Luc, Nguyen Huu Can
Abstract
Abstract In this work, we study an initial value problem for a system of nonlinear parabolic pseudo equations with Caputo fractional derivative. Here, we discuss the continuity which is related to a fractional order derivative. To overcome some of the difficulties of this problem, we need to evaluate the relevant quantities of the Mittag-Leffler function by constants independent of the derivative order. Moreover, we present an example to illustrate the theory.
Topics & Concepts
Fractional calculusMathematicsDerivative (finance)Nonlinear systemMathematical analysisOrdinary differential equationMittag-Leffler functionPartial differential equationOrder (exchange)Time derivativeFunction (biology)Applied mathematicsParabolic partial differential equationWork (physics)Partial derivativeInitial value problemDifferential equationPhysicsEconomicsFinanceQuantum mechanicsEvolutionary biologyBiologyThermodynamicsFinancial economicsFractional Differential Equations SolutionsNonlinear Differential Equations AnalysisDifferential Equations and Numerical Methods