scholarly journals Application of local meshless method for the solution of two term time fractional-order multi-dimensional PDE arising in heat and mass transfer

2020 ◽  
Vol 24 (Suppl. 1) ◽  
pp. 95-105 ◽  
Author(s):  
Imtiaz Ahmad ◽  
Hijaz Ahmad ◽  
Mustafa Inc ◽  
Shao-Wen Yao ◽  
Bandar Almohsen
Keyword(s):  
Mass Transfer ◽  
Fractional Derivative ◽  
Fractional Order ◽  
Caputo Fractional Derivative ◽  
Meshless Method ◽  
Fractional Part ◽  
Higher Dimensions ◽  
Numerical Treatment ◽  
Dimensional Diffusion ◽  
Derivatives Of

In this article, we presented an efficient local meshless method for the numerical treatment of two term time fractional-order multi-dimensional diffusion PDE. The demand of meshless techniques increment because of its meshless nature and simplicity of usage in higher dimensions. This technique approximates the solu?tion on set of uniform and scattered nodes. The space derivatives of the models are discretized by the proposed meshless procedure though the time fractional part is discretized by Liouville-Caputo fractional derivative. The numerical re?sults are obtained for 1-, 2- and 3-D cases on rectangular and non-rectangular computational domains which verify the validity, efficiency and accuracy of the method.

scholarly journals Application of local meshless method for the solution of two term time fractional-order multi-dimensional PDE arising in heat and mass transfer

2020 ◽  
Vol 24 (Suppl. 1) ◽  
pp. 95-105 ◽  
Author(s):  
Imtiaz Ahmad ◽  
Hijaz Ahmad ◽  
Mustafa Inc ◽  
Shao-Wen Yao ◽  
Bandar Almohsen
Keyword(s):  
Mass Transfer ◽  
Fractional Derivative ◽  
Fractional Order ◽  
Caputo Fractional Derivative ◽  
Meshless Method ◽  
Fractional Part ◽  
Higher Dimensions ◽  
Numerical Treatment ◽  
Dimensional Diffusion ◽  
Derivatives Of

In this article, we presented an efficient local meshless method for the numerical treatment of two term time fractional-order multi-dimensional diffusion PDE. The demand of meshless techniques increment because of its meshless nature and simplicity of usage in higher dimensions. This technique approximates the solu?tion on set of uniform and scattered nodes. The space derivatives of the models are discretized by the proposed meshless procedure though the time fractional part is discretized by Liouville-Caputo fractional derivative. The numerical re?sults are obtained for 1-, 2- and 3-D cases on rectangular and non-rectangular computational domains which verify the validity, efficiency and accuracy of the method.

scholarly journals Numerical simulation of three-dimensional fractional-order convection-diffusion PDEs by a local meshless method

2020 ◽  
pp. 210-210 ◽  
Author(s):  
Mohan Srivastava ◽  
Hijaz Ahmad ◽  
Imtiaz Ahmad ◽  
Phatiphat Thounthong ◽  
Nawaz Khan
Keyword(s):  
Numerical Simulation ◽  
Fractional Derivative ◽  
Meshless Method ◽  
Three Dimensional ◽  
Fractional Part ◽  
Higher Dimensions ◽  
Test Problems ◽  
Numerical Treatment ◽  
Convection Diffusion ◽  
Derivatives Of

In this article, we present an efficient local meshless method for the numerical treatment of three-dimensional convection-diffusion PDEs. The demand of meshless techniques increment because of its meshless nature and simplicity of usage in higher dimensions. This technique approximates the solution on set of uniform and scattered nodes. The space derivatives of the models are discretized by the proposed meshless procedure though the time fractional part is discretized by Liouville-Caputo fractional derivative. Some test problems on regular and irregular computational domains are presented to verify the validity, efficiency and accuracy of the method.

scholarly journals Solution of Multi-Term Time-Fractional PDE Models Arising in Mathematical Biology and Physics by Local Meshless Method

Symmetry ◽  
2020 ◽  
Vol 12 (7) ◽  
pp. 1195 ◽  
Author(s):  
Imtiaz Ahmad ◽  
Hijaz Ahmad ◽  
Phatiphat Thounthong ◽  
Yu-Ming Chu ◽  
Clemente Cesarano
Keyword(s):  
Meshless Method ◽  
Three Dimensional ◽  
Fractional Part ◽  
Diffusion Equations ◽  
Numerical Treatment ◽  
Physical Processes ◽  
Dimensional Diffusion ◽  
Symmetry Properties ◽  
Fractional Pde ◽  
Fractional Differential

Fractional differential equations depict nature sufficiently in light of the symmetry properties which describe biological and physical processes. This article is concerned with the numerical treatment of three-term time fractional-order multi-dimensional diffusion equations by using an efficient local meshless method. The space derivative of the models is discretized by the proposed meshless procedure based on the multiquadric radial basis function though the time-fractional part is discretized by Liouville–Caputo fractional derivative. The numerical results are obtained for one-, two- and three-dimensional cases on rectangular and non-rectangular computational domains which verify the validity, efficiency and accuracy of the method.

scholarly journals Correction: FRACTIONAL ORDER BARBALAT’S LEMMA AND ITS APPLICATIONS IN THE STABILITY OF FRACTIONAL ORDER NONLINEAR SYSTEMS

2017 ◽  
Vol 22 (4) ◽  
pp. 503-513 ◽  
Author(s):  
Fei Wang ◽  
Yongqing Yang
Keyword(s):  
Nonlinear Systems ◽  
Fractional Derivative ◽  
Fractional Order ◽  
Caputo Fractional Derivative ◽  
Barbalat’S Lemma ◽  
Liouville Derivative ◽  
Liouville Fractional Derivative ◽  
The Stability ◽  
The Relationship ◽  
Theoretical Results

This paper investigates fractional order Barbalat’s lemma and its applications for the stability of fractional order nonlinear systems with Caputo fractional derivative at first. Then, based on the relationship between Caputo fractional derivative and Riemann-Liouville fractional derivative, fractional order Barbalat’s lemma with Riemann-Liouville derivative is derived. Furthermore, according to these results, a set of new formulations of Lyapunov-like lemmas for fractional order nonlinear systems are established. Finally, an example is presented to verify the theoretical results in this paper.

Fractional derivatives of multidimensional Colombeau generalized stochastic processes

2013 ◽  
Vol 16 (4) ◽  
Author(s):  
Danijela Rajter-Ćirić ◽  
Mirjana Stojanović
Keyword(s):  
Stochastic Process ◽  
Fractional Derivative ◽  
Stochastic Processes ◽  
Compact Support ◽  
Caputo Fractional Derivative ◽  
Fractional Derivatives ◽  
One Dimensional ◽  
Compactly Supported ◽  
Derivatives Of ◽  
Do So

AbstractWe consider fractional derivatives of a Colombeau generalized stochastic process G defined on ℝn. We first introduce the Caputo fractional derivative of a one-dimensional Colombeau generalized stochastic process and then generalize the procedure to the Caputo partial fractional derivatives of a multidimensional Colombeau generalized stochastic process. To do so, the Colombeau generalized stochastic process G has to have a compact support. We prove that an arbitrary Caputo partial fractional derivative of a compactly supported Colombeau generalized stochastic process is a Colombeau generalized stochastic process itself, but not necessarily with a compact support.

scholarly journals A Note on Fractional Order Derivatives and Table of Fractional Derivatives of Some Special Functions

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Abdon Atangana ◽  
Aydin Secer
Keyword(s):  
Fractional Derivative ◽  
Fractional Order ◽  
Fractional Derivatives ◽  
Special Functions ◽  
Advantages And Disadvantages ◽  
Derivatives Of

The purpose of this note is to present the different fractional order derivatives definition that are commonly used in the literature on one hand and to present a table of fractional order derivatives of some functions in Riemann-Liouville sense On other the hand. We present some advantages and disadvantages of these fractional derivatives. And finally we propose alternative fractional derivative definition.

A GENERAL COMPARISON PRINCIPLE FOR CAPUTO FRACTIONAL-ORDER ORDINARY DIFFERENTIAL EQUATIONS

Fractals ◽  
2020 ◽  
Vol 28 (04) ◽  
pp. 2050070 ◽  
Author(s):  
CONG WU
Keyword(s):  
Differential Equations ◽  
Fractional Derivative ◽  
Ordinary Differential Equations ◽  
Fractional Order ◽  
Comparison Principle ◽  
Caputo Fractional Derivative ◽  
Fractional Derivatives ◽  
Fractional Order Systems ◽  
Caputo Fractional Derivatives ◽  
Full Result

In this paper, we work on a general comparison principle for Caputo fractional-order ordinary differential equations. A full result on maximal solutions to Caputo fractional-order systems is given by using continuation of solutions and a newly proven formula of Caputo fractional derivatives. Based on this result and the formula, we prove a general fractional comparison principle under very weak conditions, in which only the Caputo fractional derivative is involved. This work makes up deficiencies of existing results.

scholarly journals Impulsive partial hyperbolic differential inclusions of fractional order

2010 ◽  
Vol 43 (4) ◽  
Author(s):  
Saïd Abbas ◽  
Mouffak Benchohra
Keyword(s):  
Fixed Point ◽  
Fractional Derivative ◽  
Fractional Order ◽  
Caputo Fractional Derivative ◽  
Differential Inclusions ◽  
Fixed Point Theorems ◽  
Existence Of Solutions ◽  
Hyperbolic Differential Inclusions

AbstractIn this paper we investigate the existence of solutions of a class of partial impulsive hyperbolic differential inclusions involving the Caputo fractional derivative. Our main tools are appropriate fixed point theorems from multivalued analysis.

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