671 research outputs found
Inverse Problems of Determining Sources of the Fractional Partial Differential Equations
In this chapter, we mainly review theoretical results on inverse source
problems for diffusion equations with the Caputo time-fractional derivatives of
order . Our survey covers the following types of inverse
problems: 1. determination of time-dependent functions in interior source terms
2. determination of space-dependent functions in interior source terms 3.
determination of time-dependent functions appearing in boundary condition
Inverse Problems of Determining Coefficients of the Fractional Partial Differential Equations
When considering fractional diffusion equation as model equation in analyzing
anomalous diffusion processes, some important parameters in the model, for
example, the orders of the fractional derivative or the source term, are often
unknown, which requires one to discuss inverse problems to identify these
physical quantities from some additional information that can be observed or
measured practically. This chapter investigates several kinds of inverse
coefficient problems for the fractional diffusion equation
Fractional Fokker-Planck dynamics: Numerical algorithm and simulations
Anomalous transport in a tilted periodic potential is investigated
numerically within the framework of the fractional Fokker-Planck dynamics via
the underlying CTRW. An efficient numerical algorithm is developed which is
applicable for an arbitrary potential. This algorithm is then applied to
investigate the fractional current and the corresponding nonlinear mobility in
different washboard potentials. Normal and fractional diffusion are compared
through their time evolution of the probability density in state space.
Moreover, we discuss the stationary probability density of the fractional
current values.Comment: 10 pages, 9 figure
Ecuaciones diferenciales fraccionarias y problemas inversos.
DiagramasOur goal is the study of identification problems in the framework of transport equations with
fractional derivatives. We consider time fractional diffusion equations and space fractional
advection dispersion equations. The majority of inverse problems are ill-posed and require
regularization. In this thesis we implement one and two dimensional discrete mollification
as regularization procedures.
The main original results are located in chapters 4 and 5 but chapter 2 and the appendices
contain other material studied for the thesis, including several original proofs.
The selected software tool is MATLAB and all the routines for numerical examples are
original. Thus, the routines are part of the original results of the thesis.
Chapters 1, 2 and 3 are introductions to the thesis, inverse problems and fractional derivatives
respectively. They are survey chapters written specifically for this thesis.Nuestro objetivo es el estudio de problemas de identificación en el marco de ecuaciones de transporte con derivadas fraccionarias. Consideramos ecuaciones difusivas con derivada temporal fraccionaria y ecuaciones de advección dispersión con derivada espacial fraccionaria. La mayoría de los problemas inversos son mal condicionados y requieren regularización. En esta tesis implementamos procedimientos de regularización basados en molificación discreta en una y dos dimensiones. Los principales resultados originales se encuentran en los capítulos 4 y 5 pero el capítulo 2 y los apéndices contienen material adicional estudiado para la tesis incluídas varias demostra- ciones originales. La herramienta de software escogida es MATLAB y todas las rutinas para los ejemplos numéricos son originales, de manera que las rutinas son parte de los resultados originales de la tesis. Los capítulos 1, 2 y 3 son introductorios a la tesis, a los problemas inversos y a las derivadas fraccionarias respectivamente. Se trata de capítulos monográficos escritos especialmente para esta tesis. (Texto tomado de la fuente)Convocatoria 647 de ColcienciasDoctoradoDoctor en Ciencias - MatemáticasAnálisis Numéric
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