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Several abstract model problems of elliptic and parabolic type with inhomogeneous initial and boundary data are discussed. By means of a variant of the Dore-Venni theorem, real and complex interpolation, and trace theorems, optimal -regularity is shown. By means of this purely operator theoretic approach, classical results on -regularity of the diffusion equation with inhomogeneous Dirichlet or Neumann or Robin condition are recovered. An application to a dynamic boundary value problem with surface...
MSC 2010: 26A33, 33E12, 35B45, 35B50, 35K99, 45K05 Dedicated to Professor Rudolf Gorenflo
on the occasion of his 80th anniversaryIn the paper, maximum principle for the generalized time-fractional diffusion equations including the multi-term diffusion equation and the diffusion equation of distributed order is formulated and discussed. In these equations, the time-fractional derivative is defined in the Caputo sense. In contrast to the Riemann-Liouville fractional derivative, the Caputo fractional...
Using the Darbo fixed point theorem associated with the measure of noncompactness, we establish the existence of monotonic integrable solution on a half-line ℝ₊ for a nonlinear quadratic functional integral equation.
Mathematics Subject Classification: 65C05, 60G50, 39A10, 92C37In this paper the multi-dimensional Monte-Carlo random walk simulation
models governed by distributed fractional order differential equations
(DODEs) and multi-term fractional order differential equations are constructed.
The construction is based on the discretization leading to a generalized
difference scheme (containing a finite number of terms in the time
step and infinite number of terms in the space step) of the Cauchy problem
for...
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