Sine‐cosine wavelet method for fractional oscillator equations

2019 ◽  
Vol 42 (18) ◽  
pp. 6960-6971 ◽  
Author(s):  
Amir Saeed ◽  
Umer Saeed
Keyword(s):  
Wavelet Method ◽  
Fractional Oscillator ◽  
Oscillator Equations

A Nonlinear Fractional Oscillator and Its Experimental Identification in Terms of Wavelet Method

2011 ◽  
Author(s):  
Liviu Bereteu ◽  
Gheorghe Eugen Drăgănescu ◽  
Dan Viorel Stănescu ◽  
Madalin Bunoiu ◽  
Iosif Malaescu
Keyword(s):  
Wavelet Method ◽  
Experimental Identification ◽  
Fractional Oscillator

Solution of fractional oscillator equations using ultraspherical wavelets

2019 ◽  
Vol 16 (05) ◽  
pp. 1950075
Author(s):  
Firdous A. Shah ◽  
Rustam Abass
Keyword(s):  
Operational Matrix ◽  
Mathematical Physics ◽  
Test Problems ◽  
Algebraic Equations ◽  
Block Pulse Functions ◽  
Fractional Oscillator ◽  
Oscillator Type ◽  
General Order ◽  
Model Equations ◽  
Oscillator Equations

Fractional oscillator type equations are well-known model equations to describe several phenomenon in mathematical physics, engineering and biology. In this paper, a new method incorporated by the ultraspherical wavelet operational matrix of general order integration and block-pulse functions are adopted to investigate the solution of fractional oscillator type equations. To facilitate this, the ultraspherical wavelets are first presented and the corresponding operational matrix of fractional-order integration is derived by virtue of block pulse functions. The properties of ultraspherical wavelets and block pulse functions are used to transform the underlying problem to a system of algebraic equations which can be easily solved by any of the usual numerical methods. The efficiency and accuracy of the proposed method is demonstrated by presenting several benchmark test problems. Moreover, special attention is given to the comparison of the numerical results obtained by the new algorithm with those found by other known methods.

scholarly journals Fibonacci wavelet method for solving time-fractional telegraph equations with Dirichlet boundary conditions

2021 ◽  
pp. 104123
Author(s):  
Firdous A. Shah ◽  
Mohd Irfan ◽  
Kottakkaran S. Nisar ◽  
R.T. Matoog ◽  
Emad E. Mahmoud
Keyword(s):  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Dirichlet Boundary Conditions ◽  
Wavelet Method ◽  
Telegraph Equations
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