We present a survey of fractional differential equations and in particular of the computational cost for their numerical solutions from the view of computer science. The computational complexities of time fractional, space fractional, and space-time fractional equations are O(N2M), O(NM2), and O(NM(M + N)) compared with O(MN) for the classical partial differential equations with finite difference methods, where M, N are the number of space grid points and time steps. The potential solutions for this challenge include, but are not limited to, parallel computing, memory access optimization (fractional precomputing operator), short memory principle, fast Fourier transform (FFT) based solutions, alternating direction implicit method, multigrid ...
Fractional diffusion equations model phenomena exhibiting anomalous diffusion that can not b...
Fractional diffusion equations model phenomena exhibiting anomalous diffusion that can not b...
It is very time consuming to solve fractional differential equations. The computational complexity o...
Fractional calculus is the generalization of integer-order calculus to rational order. This subject ...
Solving differential equations of fractional (i.e., non-integer) order in an accurate, reliable and ...
Solving differential equations of fractional (i.e., non-integer) order in an accurate, reliable and ...
Fractional Calculus can be thought of as a generalisation of conventional calculus in the sense that...
AbstractIn this paper, two efficient numerical methods for solving system of fractional differential...
none3siMany problems in science and technology can be cast using differential equations with both fr...
This paper discusses the development of efficient algorithms for a certain fractional differential e...
In this review paper, the finite difference methods (FDMs) for the fractional differential equations...
This article is not available through ChesterRep.This article discusses the development of efficient...
This paper discusses the development of efficient algorithms for a certain fractional differential e...
Abstract. Many problems in science and technology can be cast using differential equations with both...
Many recently developed models in areas like viscoelasticity, electrochemistry, diffusion processes,...
Fractional diffusion equations model phenomena exhibiting anomalous diffusion that can not b...
Fractional diffusion equations model phenomena exhibiting anomalous diffusion that can not b...
It is very time consuming to solve fractional differential equations. The computational complexity o...
Fractional calculus is the generalization of integer-order calculus to rational order. This subject ...
Solving differential equations of fractional (i.e., non-integer) order in an accurate, reliable and ...
Solving differential equations of fractional (i.e., non-integer) order in an accurate, reliable and ...
Fractional Calculus can be thought of as a generalisation of conventional calculus in the sense that...
AbstractIn this paper, two efficient numerical methods for solving system of fractional differential...
none3siMany problems in science and technology can be cast using differential equations with both fr...
This paper discusses the development of efficient algorithms for a certain fractional differential e...
In this review paper, the finite difference methods (FDMs) for the fractional differential equations...
This article is not available through ChesterRep.This article discusses the development of efficient...
This paper discusses the development of efficient algorithms for a certain fractional differential e...
Abstract. Many problems in science and technology can be cast using differential equations with both...
Many recently developed models in areas like viscoelasticity, electrochemistry, diffusion processes,...
Fractional diffusion equations model phenomena exhibiting anomalous diffusion that can not b...
Fractional diffusion equations model phenomena exhibiting anomalous diffusion that can not b...
It is very time consuming to solve fractional differential equations. The computational complexity o...