Shifted fractional order Gegenbauer wavelets method for solving electrical circuits model of fractional order
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Date
2023-10
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Abstract
This study introduces a novel numerical approach based on shifted fractional-order Gegenbauer wavelets. The
technique aims to provide approximate solutions for a certain class of extremely significant fractional models
of electrical LC , RC , RL, and RLC circuits. We use a collocated approach to generate numerical solutions
for these circuits model by making use of the beneficial characteristics of shifted fractional-order Gegenbauer
polynomials (SFGBP). We include a parameter that characterizes the presence of fractional structures inside the
models in order to retain the dimensional properties of the physical parameters in the electrical circuits. Several
particular instances of the various source terms have also been examined. The main findings include the close
resemblance of current fractional-order models to classical cases, variations in current with resistance values,
and error reduction through additional series terms. Numerical simulations are shown through geometrical
interpretation to illustrate the exactness and reliability of our technique.