Fractional order continuity of a time semi-linear fractional diffusion-wave system
Nguyen Duc Phuong, Luu Vu Cam Hoan, Erdal Karapınar, Jagdev Singh, Ho Duy Binh, Nguyen Huu Can
Abstract
In this work, we consider the time-fractional diffusion equations depend on fractional orders. In more detail, we study on the initial value problems for the time semi-linear fractional diffusion-wave system and discussion about continuity with respect to the fractional derivative order. We find the answer to the question: When the fractional orders get closer, are the corresponding solutions close? To answer this question, we present some depth theories on PDEs and fractional calculus. In addition, we add an example numerical to verify the proposed theory.
Topics & Concepts
Fractional calculusOrder (exchange)MathematicsDiffusionAnomalous diffusionApplied mathematicsTime derivativeMathematical analysisCalculus (dental)PhysicsComputer scienceFinanceKnowledge managementInnovation diffusionThermodynamicsEconomicsMedicineDentistryFractional Differential Equations SolutionsNonlinear Differential Equations AnalysisDifferential Equations and Numerical Methods