Add to ORKG当前,对含有非整数阶导数和积分的方程的研究正引起越来越多学者的关注,这类分数阶导数和积分将广泛应用于科学和工程的各个领域.在标准扩散方程中用α(0<α≤1)阶分数阶导数替代一阶导数,用β(0<β≤2)阶分数阶导数替代二阶导数,得到空间-时间分数阶扩散方程.近年来,许多学者研究了空间-时间分数阶扩散方程,时间分数阶扩散-波动方程,时间分数阶扩散方程,空间分数阶扩散方程,时间分数阶对流-扩散方程,以及空间分数阶对流-扩散方程.A time fractional diffusion-reaction equation is obtained from the standard diffusion-reaction equation by replaciong the first-order derivative in time by a fractional diffusion-reaction in time of order α(0 <α≥1). In the paper, time fractional diffusion-reaction problems in half-space(for initial-value problem and mixed problem)and in whole-space(for Cauchy problem)are considered, respectively.Using Mellin and Laplace transforms,and properties of the Fox functions,the complete solutions of these time fractional diffusion-reaction...
Abstract The time fractional diffusion equation with appropriate initial and boundary conditions in ...
Fractional differential systems model many dynamical phenomena all associated with memory aspects. T...
AbstractThe solutions of the space–time fractional diffusion equations and that of the space–time fr...
Дифузионо-таласна једначина разломљеног реда по веременској променљивој добија се из класичне дифузи...
1 引言分数阶微分方程产生于一些反常扩散模型,已经被利用于模拟在工程,物理,化学和其它科学领域的许多现象．目前已有许多研究专家学者[1][2][3][4]从理论上对方程进行了研究．数值解方面,刘发旺教...
"LLC book introduces the theory and numerical methods in many areas of engineering and scientific re...
학위논문 (석사)-- 서울대학교 대학원 : 수학교육과, 2012. 2. 정상권.비선형 항을 포한하는 프랙셔널 분산 방정식은 자연현상에 관한 연구에 유용한 도구이다. 이 논문에서는 ...
An efficient strategy for the numerical solution of time-fractional diffusion-reaction problems is d...
The solution of a Caputo time fractional diffusion equation of order 0<α<10<α<1 is expressed in term...
分数阶微分方程在许多应用科学上比整数阶微分方程更能准确地模拟自然现象.本文考虑分数阶反应-扩散方程.将一阶的时间偏导数用Caputo分数阶导数替换,并给出了一个隐式的差分格式.利用能量方法给出此差分格...
The time-fractional diffusion-wave equation is revisited, where the time derivative is of order 2 ν ...
We consider a time and space-symmetric fractional diffusion equation (TSS-FDE) under homogeneous Dir...
AbstractFractional diffusion equations are useful for applications in which a cloud of particles spr...
In this paper, we get exact solution of the time-fractional advection-dispersion equation with react...
The solutions of the space–time fractional diffusion equations and that of the space–time fractional...
Abstract The time fractional diffusion equation with appropriate initial and boundary conditions in ...
Fractional differential systems model many dynamical phenomena all associated with memory aspects. T...
AbstractThe solutions of the space–time fractional diffusion equations and that of the space–time fr...
Дифузионо-таласна једначина разломљеног реда по веременској променљивој добија се из класичне дифузи...
1 引言分数阶微分方程产生于一些反常扩散模型,已经被利用于模拟在工程,物理,化学和其它科学领域的许多现象．目前已有许多研究专家学者[1][2][3][4]从理论上对方程进行了研究．数值解方面,刘发旺教...
"LLC book introduces the theory and numerical methods in many areas of engineering and scientific re...
학위논문 (석사)-- 서울대학교 대학원 : 수학교육과, 2012. 2. 정상권.비선형 항을 포한하는 프랙셔널 분산 방정식은 자연현상에 관한 연구에 유용한 도구이다. 이 논문에서는 ...
An efficient strategy for the numerical solution of time-fractional diffusion-reaction problems is d...
The solution of a Caputo time fractional diffusion equation of order 0<α<10<α<1 is expressed in term...
分数阶微分方程在许多应用科学上比整数阶微分方程更能准确地模拟自然现象.本文考虑分数阶反应-扩散方程.将一阶的时间偏导数用Caputo分数阶导数替换,并给出了一个隐式的差分格式.利用能量方法给出此差分格...
The time-fractional diffusion-wave equation is revisited, where the time derivative is of order 2 ν ...
We consider a time and space-symmetric fractional diffusion equation (TSS-FDE) under homogeneous Dir...
AbstractFractional diffusion equations are useful for applications in which a cloud of particles spr...
In this paper, we get exact solution of the time-fractional advection-dispersion equation with react...
The solutions of the space–time fractional diffusion equations and that of the space–time fractional...
Abstract The time fractional diffusion equation with appropriate initial and boundary conditions in ...
Fractional differential systems model many dynamical phenomena all associated with memory aspects. T...
AbstractThe solutions of the space–time fractional diffusion equations and that of the space–time fr...