scholarly journals Fractional Order Operational Matrix Method for Solving Two-Dimensional Nonlinear Fractional Volterra Integro-Differential Equations

2021 ◽  
Vol 45 (4) ◽  
pp. 571-585
Author(s):  
AMIRAHMAD KHAJEHNASIRI ◽  
◽  
M. AFSHAR KERMANI ◽  
REZZA EZZATI ◽  
◽  
...  
Keyword(s):  
Integral Equation ◽  
Differential Equations ◽  
Fractional Order ◽  
Volterra Integral Equation ◽  
Matrix Method ◽  
Operational Matrix ◽  
Basis Functions ◽  
Two Dimensional ◽  
Numerical Examples ◽  
Operational Matrix Method

This article presents a numerical method for solving nonlinear two-dimensional fractional Volterra integral equation. We derive the Hat basis functions operational matrix of the fractional order integration and use it to solve the two-dimensional fractional Volterra integro-differential equations. The method is described and illustrated with numerical examples. Also, we give the error analysis.

Haar Wavelet Operational Matrix Method for the Numerical Solution of Fractional Order Differential Equations

2015 ◽  
Vol 4 (4) ◽  
Author(s):  
Firdous A. Shah ◽  
R. Abbas
Keyword(s):  
Differential Equations ◽  
Fractional Order ◽  
Matrix Method ◽  
Present Method ◽  
Operational Matrix ◽  
Haar Wavelet ◽  
Haar Wavelets ◽  
Operational Matrix Method ◽  
Fractional Order Differential Equations ◽  
Block Pulse Functions

AbstractIn this paper, we propose a new operational matrix method of fractional order integration based on Haar wavelets to solve fractional order differential equations numerically. The properties of Haar wavelets are first presented. The properties of Haar wavelets are used to reduce the system of fractional order differential equations to a systemof algebraic equationswhich can be solved numerically byNewton’s method.Moreover, the proposed method is derived without using the block pulse functions considered in open literature and does not require the inverse of the Haar matrices. Numerical examples are included to demonstrate the validity and applicability of the present method.

scholarly journals Legendre Wavelet Operational Matrix Method for Solution of Riccati Differential Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
S. Balaji
Keyword(s):  
Differential Equations ◽  
Fractional Order ◽  
Existence And Uniqueness ◽  
Matrix Method ◽  
Operational Matrix ◽  
Computational Effort ◽  
Algebraic Equations ◽  
Riccati Differential Equation ◽  
Operational Matrix Method ◽  
Riccati Differential Equations

A Legendre wavelet operational matrix method (LWM) is presented for the solution of nonlinear fractional-order Riccati differential equations, having variety of applications in quantum chemistry and quantum mechanics. The fractional-order Riccati differential equations converted into a system of algebraic equations using Legendre wavelet operational matrix. Solutions given by the proposed scheme are more accurate and reliable and they are compared with recently developed numerical, analytical, and stochastic approaches. Comparison shows that the proposed LWM approach has a greater performance and less computational effort for getting accurate solutions. Further existence and uniqueness of the proposed problem are given and moreover the condition of convergence is verified.

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