Transparent Boundary Conditions for a Diffusion Problem Modified by Hilfer Derivative

Journal of Mathematical Sciences

Ghanam, Ryad A.¹  Malik, Nadeem A.¹  Tatar, Nasser-eddine¹ 

关键词: Caputo fractional derivative;    Hilfer fractional derivative;    fractional diffusion problem;    Mittag-Leffler function;    artificial boundary condition;    reduced equivalent problem.;   

DOI  :  

学科分类：数学（综合）

来源: University of Tokyo * Department of Mathematical Sciences

【 摘 要 】

Weconsiderahomogeneousfractionaldiffusionprobleminaninfinitereservoirsometimescalleda``modified"diffusionequation.Theequationinvolvesa(nonlocalintime)memorytermintheformofatimefractionalderivative(oftheLaplacian).Forthesakeofreducingthecomputationaldomaintoaboundedoneweestablishappropriate``artificial"boundaryconditions.Thisistoavoidtheeffectofreflectedwavesincaseofa``solid"standardboundary.Then,anequivalentproblemisstudiedinthisboundeddomain.TothisendweusetheLaplace-Fouriertransform,thetwo-parameterMittag-Lefflerfunctionandsomepropertiesoffractionalderivatives.

【 授权许可】

Unknown