Jñānābha‎, Vol. 51 (1) (2021), (79-87)

SOLVING FRACTIONAL DIFFERENTIAL EQUATIONS CHARACTERIZING THE DYNAMICS OF A CURRENT COLLECTION SYSTEM FOR AN ELECTRIC

LOCOMOTIVE USING SHANNON WAVELET


By

Devendra Chouhan

Department of Mathematics Symbiosis University of Applied Sciences, Indore-453112, Madhya Pradesh, India.

Email:dchouhan100@gmail.com

R. S. Chandel

Department of Mathematics Government Geetanjali Girls College, Bhopal-462038, Madhya Pradesh, India.

Email:rs_chandel2009@yahoo.co.in

Uday Dolas

Department of Mathematics C. S. A. Government Postgraduate College, Sehore-466001, Madhya Pradesh, India.

Email:udolas@gmail.com

(Received : December 12, 2020 ; Revised in final form : March 22, 2021)


Abstract

In this paper, Shannon Wavelet Method (SWM) under certain conditions is proposed so as to numerically integrate a system of non-linear time invariant fractional differential equations and characterize the dynamics of a current collection system for an electric locomotive. Shannon wavelets operational matrices of integration and the Shannon Stretch Matrix (SSM) are utilized to tackle the fractional differential equations containing a term with a stretched argument. Numerical examples are provided to demonstrate the accuracy, efficiency and simplicity of the proposed Shannon wavelet method.


2010 Mathematics Subject Classifications: 42C40, 65L10, 34A08.

Keywords and phrases: Shannon wavelet, Operational matrix of integration, Shannon stretch matrix, Non-linear time invariant fractional differential equations.


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