Alejandría - Historia
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First and second fundamental solutions of the time-fractional telegraph equation with Laplace or Dirac operators
... the multidimensional time- fractional equation with Laplace or Dirac operators, where the two time-fractional derivatives of orders α ∈]0, 1] and β ∈]1, 2] are in the Caputo ...
First and second fundamental solutions of the time-fractional telegraph equation of order 2α
... the multidimensional time-fractional equation of order 2α, α ∈]0, 1], where the two time-fractional derivatives are in the Caputo ...
Multidimensional time fractional diffusion equation
... In this paper we present integral and series representations for the fundamental solution of the time fractional diffusion equation in an arbitrary dimension. The series representation obtained ...
Fundamental solution of the multi-dimensional time fractional telegraph equation
... inhomogeneous time-fractional telegraph equation with Caputo derivatives, and obtained a general representation of regular solution in rectangular domain in terms of fundamental solution and ...
The stability and stabilization of infinite dimensional Caputo-time fractional differential linear systems
... order. Fractional order calculus has become very popular in recent years, due to its demonstrated applications in many fields of applied sciences and engineering, such as the spread of contaminants in underground ...
Liao’s method for a few space and time fractional reaction-diffusion equations arising in Engineering
... Abstract— In this paper, we have applied an accurate and efficient homotopy analysis method (HAM) to find the approximate/analytical solutions for space and time fractional reaction- diffusion equations ...
Long-time behaviour and self-similarity in a coagulation equation with input of monomers
... posed by Becker and D¨ oring amounted to [6, 28], since they considered the case where the concentration of monomers stay constant in time. Physically this can only be implemented by coupling the system to a ...
Regional enlarged observability of fractional differential equations with Riemann—Liouville time derivatives
... of fractional differential equations, compared with the classical theory of differential equations, is a field of research only on its initial stage of development, calling great interest to many mathematicians [ ...
Existence and uniqueness of solution for a fractional Riemann-Liouville initial value problem on time scales
... Consequently, according to the well-known theory of general metric spaces, we have for T the fundamental concepts such as open balls (intervals), neighborhoods of points, open sets, closed sets, compact sets, etc. In ...
Exact boundary control for the wave equation in a polyhedral time-dependent domain
... Littman, Near optimal time boundary controllability for a class of hyperbolic equations, In Lecture Notes in Control and Information Sciences, pp... Miranda, ContrSlabilit~ e[r] ...
An Introduction to the Fractional Continuous- Time Linear Systems: The 21
... For almost 300 years fractional derivative was seen as an interesting, but abstract, mathematical concept. The development of the fractional calculus was mainly in the hands of mathematicians. This led to a ...
On the initial conditions in continuous-time fractional linear systems
... by fractional di erential equations has been motiva- tion for the study and application of fractional calcu- ...the fractional calculus to science and engineering problems needs a coherent ...
An Introduction to the Fractional Continuous- Time Linear Systems: The 21
... vast time and frequency scales with very concise and computable models [4], [8], [12], [13], [16], [26], [29], [47]–[50], ...the fractional systems exhibits both short and long term ...of time ...
A Fractional Linear System View of the Fractional Brownian Motion
... Fractional Brownian motion (fBm), 1/f noises, self-similaririty and long range dependence are inter- connected notions and appear in a variety of contexts [1–3]. The starting point was the introduction of the fBm ...
A New Approach for Time Series Forecasting: Bayesian Enhanced by Fractional Brownian Motion with Application to Rainfall Series
... Although the comparison was performed on ANN-based filters, the experimental results confirm that the enhanced Bayesian method can predict chaotic time series more effectively in terms of SMAPE and RMSE indices ...
On The Existence Of Conditions Of a Classical Solution Of BGK-Poisson's Equation In Finite Time
... Abstract —In this paper we prove the existence of solution to the periodic Boltzmann BGK model (Bhatnagar-Gross-Krook) coupled with poisson’s equation in one space dimension. BGK model is a collision operator for ...
Fractional calculus of variations
... The roots of the calculus of variations appear in works of Greek thinkers, such as Queen Dido or Aristotle in the late of the 1st century BC. During the 17th century, some physicists and mathematicians (Galileo, Fermat, ...
Nonlinear multidimensional scaling and visualization of earthquake clusters over space, time and feature space
... Investigations on earthquake predictions are based on the assumption that all of the regional factors can be filtered out and general information about the earthquake precursory patterns can be extracted (Geller et al., ...
An implicit finite difference approximation for the solution of the diffusion equation with distributed order in time
... diffusion equation with distributed-order of derivative in time has been presented, and its unconditional stability and convergence were ...the time derivatives since it will be convenient to use ...
Existence and uniqueness results for a fractional Riemann-Liouville nonlocal thermistor problem on arbitrary time scales
... A time scale is a model of time, and the theory has found important applications in several contexts that require simultane- ous modeling of discrete and continuous ...