Application of Chebyshev Wavelet Methods for Numerical Simulation of Fractional Differential Equations

2018 ◽  
pp. 167-194
Author(s):  
Santanu Saha Ray ◽  
Arun Kumar Gupta
Keyword(s):  
Numerical Simulation ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Chebyshev Wavelet ◽  
Fractional Differential ◽  
Wavelet Methods

Approximation properties for solutions to Itô–Doob stochastic fractional differential equations with non-Lipschitz coefficients

2019 ◽  
Vol 19 (04) ◽  
pp. 1950029 ◽  
Author(s):  
Mahmoud Abouagwa ◽  
Ji Li
Keyword(s):  
Numerical Simulation ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Approximation Theorem ◽  
Averaging Principle ◽  
Mean Square ◽  
Approximation Properties ◽  
Fractional Differential ◽  
Stochastic Fractional Differential Equations

In this paper, we are concerned with the approximation theorem as an averaging principle for the solutions to stochastic fractional differential equations of Itô–Doob type with non-Lipschitz coefficients. The simplified systems will be investigated, and their solutions can be approximated to that of the original systems in the sense of mean square and probability, which constitute the approximation theorem. Two examples are presented with a numerical simulation to illustrate the obtained theory.

scholarly journals Wavelet Methods for Solving Fractional Order Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
A. K. Gupta ◽  
S. Saha Ray
Keyword(s):  
Differential Equations ◽  
Fractional Calculus ◽  
Fractional Differential Equations ◽  
Arbitrary Order ◽  
Applied Mathematics ◽  
Science And Engineering ◽  
The Past ◽  
Biological Population ◽  
Fractional Differential ◽  
Wavelet Methods

Fractional calculus is a field of applied mathematics which deals with derivatives and integrals of arbitrary orders. The fractional calculus has gained considerable importance during the past decades mainly due to its application in diverse fields of science and engineering such as viscoelasticity, diffusion of biological population, signal processing, electromagnetism, fluid mechanics, electrochemistry, and many more. In this paper, we review different wavelet methods for solving both linear and nonlinear fractional differential equations. Our goal is to analyze the selected wavelet methods and assess their accuracy and efficiency with regard to solving fractional differential equations. We discuss challenges faced by researchers in this field, and we emphasize the importance of interdisciplinary effort for advancing the study on various wavelets in order to solve differential equations of arbitrary order.

Sign in / Sign up

Export Citation Format

Share Document