On multi-periodicity in a delayed model of hematopoiesis

In this paper, the newly proposed concept of the generalized proportional fractional integral operator with respect to another function [Formula: see text] has been utilized to generate integral inequalities using convex function. This new concept will have the option to reduce self-similitudes in the fractional attractors under investigation. We discuss the implications and other consequences of the integral inequalities concerning the generalized proportional fractional integral operator with respect to another function [Formula: see text] are derived here and these outcomes permit us specifically to generalize some classical inequalities. Certain intriguing subsequent consequences of the fundamental hypotheses are also figured. It is to be supposed that this investigation will provide new directions in the quantum theory of capricious nature.

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New Estimates of Integral Inequalities via Generalized Proportional Fractional Integral Operator With Respect to Another Function

Rashid

Hammouch

Jarad

et al. 2020

Fractals

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Lyapunov stability analysis for nonlinear delay systems under random effects and stochastic perturbations with applications in finance and ecology

et al. 2021

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This manuscript is involved in the study of stability of the solutions of functional differential equations (FDEs) with random coefficients and/or stochastic terms. We focus on the study of different types of stability of random/stochastic functional systems, specifically, stochastic delay differential equations (SDDEs). Introducing appropriate Lyapunov functionals enables us to investigate the necessary conditions for stochastic stability, asymptotic stochastic stability, asymptotic mean square stability, mean square exponential stability, global exponential mean square stability, and practical uniform exponential stability. Some examples with numerical simulations are presented to strengthen the theoretical results. Using our theoretical study, important aspects of epidemiological and ecological mathematical models can be revealed. In ecology, the dynamics of Nicholson’s blowflies equation is studied. Conditions of stochastic stability and stochastic global exponential stability of the equilibrium point at which the blowflies become extinct are investigated. In finance, the dynamics of the Black–Scholes market model driven by a Brownian motion with random variable coefficients and time delay is also studied.

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On multi-periodicity in a delayed model of hematopoiesis

Cited by 2 publications

References 20 publications

New Estimates of Integral Inequalities via Generalized Proportional Fractional Integral Operator With Respect to Another Function

New Estimates of Integral Inequalities via Generalized Proportional Fractional Integral Operator With Respect to Another Function

Lyapunov stability analysis for nonlinear delay systems under random effects and stochastic perturbations with applications in finance and ecology

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