scholarly journals Complete Solution For The Time Fractional Diffusion Problem With Mixed Boundary Conditions by Operational Method

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
A. Aghili
Keyword(s):  
Heat Conduction ◽  
Boundary Conditions ◽  
Mixed Boundary ◽  
Heat Conduction Problem ◽  
Complete Solution ◽  
Mixed Boundary Conditions ◽  
Fractional Diffusion ◽  
Diffusion Problem ◽  
Two Dimensions ◽  
Operational Method

AbstractIn this study, we present some new results for the time fractional mixed boundary value problems. We consider a generalization of the Heat - conduction problem in two dimensions that arises during the manufacturing of p - n junctions. Constructive examples are also provided throughout the paper. The main purpose of this article is to present mathematical results that are useful to researchers in a variety of fields.

Fractional Sturm-Liouville Problem and 1D Space-Time Fractional Diffusion With Mixed Boundary Conditions

2015 ◽  
Author(s):  
Malgorzata Klimek
Keyword(s):  
Boundary Conditions ◽  
Mixed Boundary ◽  
Liouville Problem ◽  
Mixed Boundary Conditions ◽  
Fractional Diffusion ◽  
Diffusion Problem ◽  
Space Time ◽  
Sturm Liouville ◽  
Derivatives Of ◽  
Space Interval

In the paper, we show a connection between a regular fractional Sturm-Liouville problem with left and right Caputo derivatives of order in the range (1/2, 1) and a 1D space-time fractional diffusion problem in a bounded domain. Both problems include mixed boundary conditions in a finite space interval. We prove that in the case of vanishing mixed boundary conditions, the Sturm-Liouville problem can be rewritten in terms of Riesz derivatives. Then, we apply earlier results on its eigenvalues and eigenfunctions to construct a weak solution of the 1D fractional diffusion equation with variable diffusivity. Adding an assumption on the summability of the eigenvalues’ inverses series, we formulate a theorem on a strong solution of the 1D fractional diffusion problem.

A VISCOUS-INVISCID COUPLING UNDER MIXED BOUNDARY CONDITIONS

1992 ◽  
Vol 02 (04) ◽  
pp. 461-482 ◽  
Author(s):  
C. CANUTO ◽  
A. RUSSO
Keyword(s):  
Boundary Conditions ◽  
Original Problem ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Diffusion Problem ◽  
Convection Diffusion ◽  
Convection Equation ◽  
Convection Dominated

In this paper we consider a nonlinear modification of a linear convection-diffusion problem in order to get a pure convection equation where the original problem is convection dominated. We extend the results of previous papers by considering mixed Dirichlet/Oblique derivative boundary conditions.

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