Stability of Fractional-Order Quasi-Linear Impulsive Integro-Differential Systems with Multiple Delays

Abstract

In this paper, some novel conditions for the stability results for a class of fractional-order quasi-linear impulsive integro-differential systems with multiple delays is discussed. First, the existence and uniqueness of mild solutions for the considered system is discussed using contraction mapping theorem. Then, novel conditions for Mittag–Leffler stability (MLS) of the considered system are established by using well known mathematical techniques, and further, the two corollaries are deduced, which still gives some new results. Finally, an example is given to illustrate the applications of the results.

Editorial: Overview and Some New Directions

“…The closedness and continuity of Carathéodory weak solutions with respect to the two different parameters are obtained. Some novel conditions for the stability results for a class of fractional-order quasi-linear impulsive integro-differential systems with multiple delays are discussed by Mathiyalagan Kalidass, Shengda Zeng and Mehmet Yavuz [6]. First, the existence and uniqueness of mild solutions for the considered system are discussed using contraction mapping theorem.…”

Analysing the market for digital payments in India using the predator-prey mode

“…In order to prove the essence and significance of mathematical modelling in connection with realworld problems, the authors in [6][7][8] investigated the omicron and its earlier version and presented some useful results. The current study can be extended by generalizing the integer order derivative with fractional order; for instance, the stability of the integro-differential systems within the frame of fractional order is connected by researchers in [9], the hyper-chaotic system is examined with the help of novel fractional operator in [10], the physical model with unstable cases is investigated in [11], the numerical method for higher order fractional system is proposed by researchers in [12], the chemical reaction model is investigated with the efficient numerical scheme in [13], the scholars in [14][15][16] where the competing website can coexist. Brander and de Bettignies [23] use the predator-prey model to provide a contributing explanation for both high-venture capital concentration by industry and 'boom and bust' industry-level investment dynamics.…”

Dynamics of a stochastic epidemic-like rumor propagation model with generalized nonlinear incidence and time delay

“…On the other hand, some current studies also reveal the impact of time delay on social networks [37,38]. It follows that time delay not only affects the dynamic characteristics of the model, but also affects the stability of the system [39,40]. However, although the introduction of time delay, general incidence and other factors can morerealistically describe the rumor propagation process, the above literature has not considered the impact of uncertain environmental factors on rumor propagation.…”