In this paper, a new bio-inspired metaheuristic algorithm called Giant Armadillo Optimization (GAO) is introduced, which imitates the natural behavior of giant armadillo in wild. The fundamental inspiration design GAO derived from hunting strategy armadillos moving towards prey positions and digging termite mounds. theory expressed mathematically modeled two phases: (i) exploration based on simulating movement mounds, (ii) exploitation armadillos' skills order to rip open performance...

This paper introduces a novel nature-inspired optimization algorithm called the Addax Optimization Algorithm (AOA), which emulates natural behavior of addax in wild.The core inspiration for AOA is drawn from addax's foraging strategy and digging skills.The theoretical foundation expounded mathematically modeled two phases: (i) exploration based on modeling position change during (ii) exploitation digging.The efficiency handling realworld engineering applications evaluated four design...

Because they are useful for both enabling numerical simulations and containing well-defined physical phenomena, discrete fractional reaction–diffusion models have attracted a great deal of interest from academics. Within the family models, form is examined in detail this study. Furthermore, we investigate complex synchronization dynamics suggested master–slave system using accuracy linear control techniques combined with Lyapunov approach. This study’s deviation behavior equivalents integer...

The aim of this work is to describe the dynamics a discrete fractional-order reaction–diffusion FitzHugh–Nagumo model. We established acceptable requirements for local asymptotic stability system’s unique equilibrium. Moreover, we employed Lyapunov functional show that constant equilibrium solution globally asymptotically stable. Furthermore, numerical simulations are shown clarify and exemplify theoretical results.

Discrete fractional models with reaction-diffusion have gained significance in the scientific field recent years, not only due to need for numerical simulation but also stated biological processes. In this paper, we investigate problem of synchronization-control a discrete nonlinear bacterial culture model using Caputo h-difference operator and second-order central difference scheme an L1 finite after deriving version well-known Degn–Harrison system Lengyel–Epstein system. Using appropriate...

In the last few years, reaction–diffusion models associated with discrete fractional calculus have risen in prominence scientific fields, not just due to requirement for numerical simulation but also described biological phenomena. This work investigates a equivalent of glycolysis model. The tool is introduced modeling diffusion problems Caputo-like delta sense, and discretization model described. local stability equilibrium points proposed system examined. We additionally investigate global...

In this paper, a novel human-based metaheuristic algorithm called Actor Optimization Algorithm (AOA) is introduced. AOA mimics the behaviors of an actor when playing role. The main idea in designing derived from specific behavior including (i) simulating movements and dialogues given role (ii) practicing to better present assigned theory stated mathematically modeled phases exploration exploitation. performance address real-world applications evaluated on CEC 2011 test suite. optimization...

In this study, we expand a 2D sine map via adding the discrete memristor to introduce new 3D fractional-order sine-based map. Under commensurate and incommensurate orders, conduct an extensive exploration analysis of its nonlinear dynamic behaviors, employing diverse numerical techniques, such as analyzing Lyapunov exponents, visualizing phase portraits, plotting bifurcation diagrams. The results emphasize map’s sensitivity parameters, resulting in emergence distinct patterns. addition,...

Variable-order fractional discrete calculus is a new and unexplored part of that provides extraordinary capabilities for simulating multidisciplinary processes. Recognizing this incredible potential, the scientific community has been researching variable-order applications to modeling engineering physical systems. This research makes contribution topic by describing establishing first generalized variable order Gronwall inequality we employ examine finite time stability nonlinear Nabla...

In this paper, we define surfaces of revolution without parabolic points in three-dimensional Lorentz–Minkowski space. Then, classify class under the condition ΔIIIx=Ax, where ΔIII is Laplace operator regarding third fundamental form, and A a real square matrix order 3. We prove that such are either catenoids or Enneper, pseudo spheres hyperbolic spaces centered at origin.

In the 3-dimensional Euclidean space E3, a quadric surface is either ruled or of one following two kinds z2=as2+bt2+c,abc≠0 z=a2s2+b2t2,a>0,b>0. present paper, we investigate these three surfaces whose Gauss map N satisfies property ΔIIN=ΛN, where Λ square symmetric matrix order 3, and ΔII denotes Laplace operator second fundamental form II surface. We prove that spheres with nonzero Λ, helicoids as corresponding zero matrix, are only classes satisfying above given property.

The paper introduces a novel two-dimensional fractional discrete-time predator–prey Leslie–Gower model with an Allee effect on the predator population. model’s nonlinear dynamics are explored using various numerical techniques, including phase portraits, bifurcations and maximum Lyapunov exponent, consideration given to both commensurate incommensurate orders. These techniques reveal that fractional-order exhibits intricate diverse dynamical characteristics, stable trajectories, periodic...

This article. in the introduction, gives a brief historic description on surfaces of finite Chen-type and coordinate according to first, second third fundamental form surface Euclidean E^3 space . Then, an important class was introduced, namely, ruled were classified its Chen type with respect form.

This paper introduces a groundbreaking metaheuristic algorithm named Magnificent Frigatebird Optimization (MFO), inspired by the unique behaviors observed in magnificent frigatebirds their natural habitats.The foundation of MFO is based on kleptoparasitic behavior these birds, where they steal prey from other seabirds.In this process, frigatebird targets food-carrying seabird, aggressively pecking at it until seabird drops its prey.The then swiftly dives to capture abandoned before falls...

In this paper, an algorithm for computing a polynomial control and Lyapunov function in the simplicial Bernstein form is developed. This ensures asymptotic stability of designed feedback system. To end, we provide certificates positivity polynomials form. Subsequently, state space partitioned into simplices. On each simplex, simultaneously compute functions. With control, equilibrium asymptotically stable.

This paper considers control synthesis for polynomial systems. The developed method leans upon Lyapunov stability and Bernstein certificates of positivity. We strive to develop an algorithm that computes a Lyaponov function in the simplicial form. Subsequently, we reduce problem finite number evaluations within coefficient bounds representing controls functions. As consequence, equilibrium is asymptotically stable with this control.

In This paper we study certain fractional forms of Abel's equation:y' = P(x) + Q <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> (x)y xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> <sup xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> . We solve the form equation for cases: 0 or 0. Such cases reduce to Bernoulli differential equation.

This paper proves several new inequalities for the Euclidean operator radius, which refine some recent results. It is shown that results are much more accurate than related, recently published Moreover, both symmetric and non-symmetric Hilbert space operators studied.