[图书][B] Mittag-Leffler functions, related topics and applications

R Gorenflo, AA Kilbas, F Mainardi, SV Rogosin - 2020 - Springer
Mittag-Leffler Functions, Related Topics and Applications Page 1 Springer Monographs in
Mathematics Rudolf Gorenflo Anatoly A. Kilbas Francesco Mainardi Sergei Rogosin Mittag-Leffler …

Initial-boundary-value problems for the generalized multi-term time-fractional diffusion equation

Y Luchko - Journal of Mathematical Analysis and Applications, 2011 - Elsevier
In this paper, the initial-boundary-value problems for the generalized multi-term time-
fractional diffusion equation over an open bounded domain G×(0, T), G∈ Rn are …

Maximum principle for the generalized time-fractional diffusion equation

Y Luchko - Journal of Mathematical Analysis and Applications, 2009 - Elsevier
In the paper, a maximum principle for the generalized time-fractional diffusion equation over
an open bounded domain G×(0, T), G⊂ Rn is formulated and proved. The proof of the …

[HTML][HTML] Some uniqueness and existence results for the initial-boundary-value problems for the generalized time-fractional diffusion equation

Y Luchko - Computers & Mathematics with Applications, 2010 - Elsevier
In this paper, some uniqueness and existence results for the solutions of the initial-boundary-
value problems for the generalized time-fractional diffusion equation over an open bounded …

Initial-boundary-value problems for the one-dimensional time-fractional diffusion equation

Y Luchko - Fractional Calculus and Applied Analysis, 2012 - Springer
In this paper, some initial-boundary-value problems for the time-fractional diffusion equation
are first considered in open bounded n-dimensional domains. In particular, the maximum …

[HTML][HTML] Modeling plant water deficit by a non-local root water uptake term in the unsaturated flow equation

M Berardi, G Girardi - … in Nonlinear Science and Numerical Simulation, 2024 - Elsevier
In this paper we present a novel way to mathematically frame the concept of ecological
memory of plant water stress in the context of root water uptake in unsaturated flow …

Variable Order Differential Equations with Piecewise Constant Order-Function and Diffusion with Changing Modes

S Umarov, S Steinberg - Zeitschrift für Analysis und ihre Anwendungen, 2009 - ems.press
In this paper diffusion processes with changing modes are studied involving the variable
order partial differential equations. We prove the existence and uniqueness theorem of a …

[图书][B] Beyond the triangle: Brownian motion, itô calculus, and Fokker-Planck equation-fractional generalizations

S Umarov, M Hahn, K Kobayashi - 2018 - books.google.com
The book is devoted to the fundamental relationship between three objects: a stochastic
process, stochastic differential equations driven by that process and their associated Fokker …

Cauchy and nonlocal multi-point problems for distributed order pseudo-differential equations: Part one

S Umarov, R Gorenflo - J. Anal. Appl, 2005 - ems.press
We treat the question of existence, uniqueness and construction of a solution to the Cauchy
and multi-point problems for a general linear evolution equation with (in general) temporal …

On fractional Duhamelʼs principle and its applications

S Umarov - Journal of Differential Equations, 2012 - Elsevier
The classical Duhamel principle, established nearly 200 years ago by Jean-Marie-Constant
Duhamel, reduces the Cauchy problem for an inhomogeneous partial differential equation to …