Shifted fractional order Gegenbauer wavelets method for solving electrical circuits model of fractional order

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 Image 1, Image 2, Image 3, and Image 4 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.

Keywords

• Block pulse function
• Caputo derivative
• Electrical circuits
• Shifted fractional-order Gegenbauer wavelets
• Shifted fractional-order Gegenbauer polynomials