Stability and dynamics of neutral and integro-differential regularized Prabhakar fractional differential systems

Abstract

In this work, we investigate the asymptotic stability analysis for two classes of nonlinear fractional systems with the regularized Prabhakar derivative. The stability analysis of the neutral and integro-differential nonlinear fractional systems are studied by assessing the eigenvalues of associated matrix and applying conditions on the nonlinear part of these types of systems. We use a numerical method to solve the fractional differential equations with the regularized Prabhakar fractional derivative. We further present the numerical simulations on several test cases to examine and reveal the complex dynamics of the analytical obtained results.

Qualitative analysis of the Prabhakar-Caputo type fractional delayed equations

“…Lemma 5. 37 For any , , > 0, the Laplace transform of the general version of Mittag-Leffler type function of three parameters  , (…”

“…Lemma 6. 37 The Laplace integral transform of Prabhakar fractional derivative of Caputo-type is represented by…”

A catalogue of semigroup properties for integral operators with Fox–Wright kernel functions

“…It has discovered a number of interesting applications, including in viscoelasticity, 22,23 nanofluids, 24 stochastic processes, 25 options pricing, 26 and anomalous dielectrics 14 . Fractional differential equations involving Prabhakar‐type operators have been analysed using various methods, including compactness of operators 27 and stability of dynamical systems 28,29 . Mathematically, what are the interesting properties of Prabhakar operators that allow such analyses to be performed?…”

“…14 Fractional differential equations involving Prabhakar-type operators have been analysed using various methods, including compactness of operators 27 and stability of dynamical systems. 28,29 Mathematically, what are the interesting properties of Prabhakar operators that allow such analyses to be performed?…”

Advances in transport phenomena with nanoparticles and generalized thermal process for vertical plate

“…Prabhakar fractional operator used to explain certain odd habits in disordered people materials that are nonlinear and nonlocal. The need for Prabhakar operators to specific fractional coefficients may be a useful tool for determining an appropriate statistical method that produced a strong agreement between theoretically and experimentally findings in [29][30][31][32][33]. For the mathematical model of variable-order fractional Volterra integral, a numerical approach focused on CCFs and the Lagrange technique is shown in [34,35].…”