Fibonacci wavelet method for time fractional convection–diffusion equations

This study concentrates on time fractional convection–diffusion equations (TFCDEs) with variable coefficients and their numerical solutions. Caputo derivative is used to calculate the time fractional order derivatives. In order to give an approximate solution to the TFCDE, an effective approach is p...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences 2024-03, Vol.47 (4), p.2639-2655
Main Authors: Yadav, Pooja, Jahan, Shah, Nisar, Kottakkaran Sooppy
Format: Article
Language:English
Subjects:
block pulse function
Convection-diffusion equation
error analysis
Fibonacci polynomial
Fibonacci wavelet
Fractional calculus
operational matrix
time‐fractional convection diffusion equations
Wavelet analysis
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Summary:This study concentrates on time fractional convection–diffusion equations (TFCDEs) with variable coefficients and their numerical solutions. Caputo derivative is used to calculate the time fractional order derivatives. In order to give an approximate solution to the TFCDE, an effective approach is proposed utilizing Fibonacci wavelet and block pulse functions. The Fibonacci wavelets operational matrices of fractional order integration are constructed. By combining the collocation technique, they are used to simplify the fractional model to a collection of algebraic equations. The suggested approach is quite practical for resolving issues of this nature. The comparison and analysis with other approaches demonstrate the effectiveness and precision of the suggested approach.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.9770