On a time fractional diffusion with nonlocal in time conditions
Nguyen Hoang Tuan, Nguyen Anh Triet, Nguyen Hoang Luc, Nguyen Duc Phuong
Abstract
Abstract In this work, we consider a fractional diffusion equation with nonlocal integral condition. We give a form of the mild solution under the expression of Fourier series which contains some Mittag-Leffler functions. We present two new results. Firstly, we show the well-posedness and regularity for our problem. Secondly, we show the ill-posedness of our problem in the sense of Hadamard. Using the Fourier truncation method, we construct a regularized solution and present the convergence rate between the regularized and exact solutions.
Topics & Concepts
MathematicsHadamard transformOrdinary differential equationTruncation (statistics)Partial differential equationMathematical analysisConvergence (economics)Applied mathematicsFourier transformMittag-Leffler functionFourier seriesDiffusionFractional calculusSeries (stratigraphy)Differential equationPhysicsBiologyEconomicsEconomic growthPaleontologyStatisticsThermodynamicsFractional Differential Equations SolutionsNonlinear Differential Equations AnalysisDifferential Equations and Boundary Problems