Pantograph, the technological successor of trolley poles, is an overhead current collector electric bus, trains, and trams. In this work, we consider discrete fractional pantograph equation form Δ∗β[k](t)=wt+β,k(t+β),k(λ(t+β)), with condition k(0)=p[k] for t∈N1−β, 0<β≤1, λ∈(0,1) investigate properties asymptotic stability solutions. We will prove main results by aid Krasnoselskii’s generalized Banach fixed point theorems. Examples involving algorithms illustrated graphs are presented to...

Abstract A human being standing upright with his feet as the pivot is most popular example of stabilized inverted pendulum. Achieving stability pendulum has become common challenge for engineers. In this paper, we consider an initial value discrete fractional Duffing equation forcing term. We establish existence, Hyers–Ulam stability, and Mittag-Leffler solutions equation. modeled by example. The values are tabulated simulated to show consistency theoretical findings.

An elastic beam equation (EBEq) described by a fourth-order fractional difference is proposed in this work with three-point boundary conditions involving the Riemann–Liouville operator. New sufficient ensuring solutions’ existence and uniqueness of problem are established. The findings obtained employing properties discrete equations, Banach contraction, Brouwer fixed-point theorems. Further, we discuss our problem’s results concerning Hyers–Ulam (HU), generalized (GHU), Hyers–Ulam–Rassias...

A mathematical model of discrete fractional equations with initial condition is constructed to study the tumor-immune interactions in this research. The a system two nonlinear difference sense Caputo operator. applications Banach's and Leray-Schauder's fixed point theorems are used analyze existence results for proposed model. Additionally, we developed several kinds Ulam's stability suggested map's dynamic behavior numerical analyzed some special cases. Further, adaptive control law...

Pantograph, a device in which an electric current is collected from overhead contact wires, introduced to increase the speed of trains or trams. The work aims study stability properties nonlinear fractional order generalized pantograph equation with discrete time, using Hilfer operator. Hybrid fixed point theorem considered existence solutions, and uniqueness solution proved Banach contraction theorem. Stability results sense Ulam Hyers, its form for initial value problem are established we...

Crimean-Congo hemorrhagic fever is a common disease between humans and animals that transmitted to through infected ticks, contact with animals, humans. In this paper, we present boxed model for the transmission of virus. With help fixed-point theory, our proposed system investigated in detail prove its unique solution. Given Caputo fractional-order derivative preserves system’s historical memory, use fractional modeling. The equilibrium points their stability conditions are determined....

Abstract The results reported in this paper are concerned with the existence and uniqueness of solutions discrete fractional order two-point boundary value problem. developed by employing properties Caputo Riemann–Liouville difference operators, contraction mapping principle Brouwer fixed point theorem. Furthermore, conditions for Hyers–Ulam stability Hyers–Ulam–Rassias proposed problem established. applicability theoretical findings has been demonstrated relevant practical examples....

Towards the end of 2019, world witnessed outbreak Severe Acute Respiratory Syndrome Coronavirus-2 (COVID-19), a new strain coronavirus that was unidentified in humans previously. In this paper, fractional-order Susceptible–Exposed–Infected–Hospitalized–Recovered (SEIHR) model is formulated for COVID-19, where population infected due to human transmission. The discrete version obtained by process discretization and basic reproductive number calculated with next-generation matrix approach. All...

<abstract> It is well known that Newton's second law can be applied in various biological processes including the behavior of vibrating eardrums. In this work, we consider a nonlinear discrete fractional initial value problem as model describing dynamic eardrum. We establish sufficient conditions for existence, uniqueness, and Hyers-Ulam stability solutions proposed model. To examine validity our findings, concrete example forced eardrum equation along with numerical simulation analyzed. </abstract>

Abstract A thermostat model described by a second-order fractional difference equation is proposed in this paper with one sensor and two sensors boundary conditions depending on positive parameters using the Lipschitz-type inequality. By means of well-known contraction mapping Brouwer fixed-point theorem, we provide new results existence uniqueness solutions. In work use Caputo operator Hyer–Ulam stability definitions check sufficient solution equations to be stable, while most researchers...

In this paper, we propose to study the SIR epidemic model of childhood disease in human population. Fractional order is considered and its discrete form obtained. Local asymptotic stability free equilibrium endemic points are discussed basic reproduction number R0 obtained via next generation matrix method. Time series plots, phase portraits, bifurcation diagram sensitive dependence on initial condions analyzed under suitable conditions. Numerical examples used verify results.

A gauss type prey - predator model is considered with Allee effect and Holling II response. Fractional order two species system discretized. The discretized exhibits much richer complex dynamics than its corresponding continuous version.Bifurcation types like flip, neimark sacker chaos exist in the system.Existence of positive fixed points established local stability discrete fractional discussed variational matrix. It also shown that allows a flip bifurcation bifurcation. Rich dynamical...

This paper investigates the oscillation of a class fractional difference equations with damping term form where denotes Riemann-Liouville operator order is quotient odd positive integers. Based on generalized Riccati transformation and some inequalities, we establish sufficient conditions criteria for it. Some applications are also presented established results.Keywords: Difference Equations, Oscillation, Fractional Order, Damping.

In this work, we establish oscillation theorems for damped fractional order difference equation of the form Δ[δ(k)Δγy(k)]+ρ(k)Δγy(k)+ξ(k)Z[Y(k)]=0,k≥k0>0 where Y(k)=∑u=k0k−1+γ(k−u−1)−γy(u) and Δγ defined as operator Riemann-Liouville derivative γ ∈ (0, 1]. By using Riccati type transformation techniques, arrive at some new sufficient conditions all solutions equation.

Due to its significance in numerous scientific and engineering domains, discrete fractional calculus (DFC) has received much attention recently. In particular, it seems that the exploration of stability DFC is crucial. A mathematical model equation describing deflection a vertical column along with two-point boundary conditions featuring Riemann–Liouville operator constructed study several kinds Ulam results this research work. addition, we developed Lyapunov-type inequality application an...

This study presents numerical examples of Discrete Fractional Order Prey Predator interactions with Functional Response. The process discretization is applied and the version discrete equations obtained. Fixed points are determined stability around fixed analyzed. Also theoretical analysis has been verified from simulations, which help better understanding proposed system. Rich dynamics system exhibited by Bifurcation diagram Periodic Oscillations for suitable parameters values. Â

In this paper we investigate the dynamical behavior of a SIR epidemic model fractional order. Disease Free Equilibrium point, Endemic point and basic reproductive number are obtained. Time series plots, phase portraits bifurcation diagrams presented for suitable parameter values. Also some numerical examples provided to illustrate dynamics system. Â

In this paper, we study the oscillatory behavior of fractionaldifference equations following form (see in paper) denotes Riemann-Liouville difference operator and η&gt;0 is a quotient odd positive integers. We establish some oscillation criteria forthe equation by using Riccati transformation technique inequalities. Anexample shown to illustrate our main results.

In this paper, we present a systematic study concerning the developments of oscillation results for fractional difference equations. Essential preliminaries on discrete calculus are stated prior to giving main results. Oscillation presented in subsequent order and different types The investigation was carried out within delta nabla operators.

In this paper, we study the complex dynamical behaviors of a discrete-time SIR epidemic model.Analysis model demonstrates that Diseases Free Equilibrium (DFE) point is globally asymptotically stable if basic reproduction number less than one while Endemic (EE) greater one.The results are further substantiated visually with numerical simulations.Furthermore, demonstrate discrete has more including multiple periodic orbits, quasi-periodic orbits and chaotic behaviors.The maximum Lyapunov...