STABILITY ANALYSIS OF DELAYED FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS WITH APPLICATIONS OF RLC CIRCUITS

Abstract

This article presents the stability analysis of integro-differential equations with a delay and a fractional order derivative via some approximation techniques for the derived nonlinear terms of characteristic exponents. Based on these techniques, the existence of some analytical solutions at the neighborhood of their equilibrium points is proved. Stability charts are constructed and so both of the critical time delay and the critical frequency formulae are obtained. The impact of this work into general RLC circuit applications containing delays and fractional order derivatives is discussed.