In biology and life sciences, fractal theory and fractional calculus have significant applications in simulating and understanding complex problems. In this paper, a compartmental model employing Caputo-type fractional and fractal-fractional operators is presented to analyze Nipah virus (NiV) dynamics and transmission. Initially, the model includes nine nonlinear ordinary differential equations that consider viral concentration, flying fox, and human populations simultaneously. The model is reconstructed using fractional calculus and fractal theory to better understand NiV transmission dynamics. We analyze the model's existence and uniqueness in both contexts and instigate the equilibrium points. The clinical epidemiology of Bangladesh is used to estimate model parameters. The fractional model's stability is examined using Ulam-Hyers and Ulam-Hyers-Rassias stabilities. Moreover, interpolation methods are used to construct computational techniques to simulate the NiV model in fractional and fractal-fractional cases. Simulations are performed to validate the stable behavior of the model for different fractal and fractional orders. The present findings will be beneficial in employing advanced computational approaches in modeling and control of NiV outbreaks.
- MeSH
- biologické modely MeSH
- infekce viry z rodu Henipavirus * epidemiologie prevence a kontrola přenos MeSH
- lidé MeSH
- počítačová simulace MeSH
- vakcinace * MeSH
- virus Nipah * imunologie MeSH
- zvířata MeSH
- Check Tag
- lidé MeSH
- zvířata MeSH
- Publikační typ
- časopisecké články MeSH
- Geografické názvy
- Bangladéš epidemiologie MeSH
Malware is a common word in modern era. Everyone using computer is aware of it. Some users have to face the problem known as Cyber crimes. Nobody can survive without use of modern technologies based on computer networking. To avoid threat of malware, different companies provide antivirus strategies on a high cost. To prevent the data and keep privacy, companies using computers have to buy these antivirus programs (software). Software varies due to types of malware and is developed on structure of malware with a deep insight on behavior of nodes. We selected a mathematical malware propagation model having variable infection rate. We were interested in examining the impact of memory effects in this dynamical system in the sense of fractal fractional (FF) derivatives. In this paper, theoretical analysis is performed by concepts of fixed point theory. Existence, uniqueness and stability conditions are investigated for FF model. Numerical algorithm based on Lagrange two points interpolation polynomial is formed and simulation is done using Matlab R2016a on the deterministic model. We see the impact of different FF orders using power law kernel. Sensitivity analysis of different parameters such as initial infection rate, variable adjustment to sensitivity of infected nodes, immune rate of antivirus strategies and loss rate of immunity of removed nodes is investigated under FF model and is compared with classical. On investigation, we find that FF model describes the effects of memory on nodes in detail. Antivirus software can be developed considering the effect of FF orders and parameters to reduce persistence and eradication of infection. Small changes cause significant perturbation in infected nodes and malware can be driven into passive mode by understanding its propagation by FF derivatives and may take necessary actions to prevent the disaster caused by cyber crimes.
- MeSH
- algoritmy * MeSH
- fraktály * MeSH
- lidé MeSH
- počítačová simulace MeSH
- software MeSH
- teoretické modely MeSH
- zabezpečení počítačových systémů * MeSH
- Check Tag
- lidé MeSH
- Publikační typ
- časopisecké články MeSH
The open nature of Wireless Sensor Networks (WSNs) renders them an easy target to malicious code propagation, posing a significant and persistent threat to their security. Various mathematical models have been studied in recent literature for understanding the dynamics and control of the propagation of malicious codes in WSNs. However, due to the inherent randomness and uncertainty present in WSNs, stochastic modeling approach is essential for a comprehensive understanding of the propagation of malicious codes in WSNs. In this paper, we formulate a general stochastic compartmental model for analyzing the dynamics of malicious code distribution in WSNs and suggest its possible control. We incorporate the stochasticity in the classical deterministic model for the inherent unpredictability in code propagation, which results in a more appropriate representation of the dynamics. A basic theoretical analysis including the stability results of the model with randomness is carried out. Moreover, a higher-order spectral collocation technique is applied for the numerical solution of the proposed stochastic model. The accuracy and numerical stability of the model is presented. Finally, a comprehensive simulation is depicted to verify theoretical results and depict the impact of parameters on the model's dynamic behavior. This study incorporates stochasticity in a deterministic model of malicious codes spread in WSNs with the implementation of spectral numerical scheme which helps to capture these networks' inherent uncertainties and complex nature.
Fractional nonlinear partial differential equations are used in many scientific fields to model various processes, although most of these equations lack closed-form solutions. For this reason, methods for approximating solutions that occasionally yield closed-form solutions are crucial for solving these equations. This study introduces a novel technique that combines the residual function and a modified fractional power series with the Elzaki transform to solve various nonlinear problems within the Caputo derivative framework. The accuracy and effectiveness of our approach are validated through analyses of absolute, relative, and residual errors. We utilize the limit principle at zero to identify the coefficients of the series solution terms, while other methods, including variational iteration, homotopy perturbation, and Adomian, depend on integration. In contrast, the residual power series method uses differentiation, and both approaches encounter difficulties in fractional contexts. Furthermore, the effectiveness of our approach in addressing nonlinear problems without relying on Adomian and He polynomials enhances its superiority over various approximate series solution techniques.
- MeSH
- algoritmy * MeSH
- nelineární dynamika * MeSH
- teoretické modely MeSH
- Publikační typ
- časopisecké články MeSH
In light of the ponderomotive force, this article focuses on establishing the exact wave structures of the ion sound system. It is the result of non-linear force and affects a charged particle oscillating in an inhomogeneous electromagnetic field. By using the Riemann-Liouville operator, β -operator, and Atangana-Baleanu fractional analysis, the examined equation-which consists of the normalized electric field of the Langmuir oscillation and normalized density perturbation-is thoroughly examined. The solutions can be obtained with the help of a relatively new integration tool, the new extended direct algebraic method. We extract various wave structures in bright, dark, combo, ark, bright, and singular soliton solutions, among other forms, from soliton solutions. This method is simple and quick, and it can be used with more non-linear models or systems. Using the Mathematica software package, a graphically comparative analysis of some solutions is also presented here, taking appropriate parametric values into consideration.
- Klíčová slova
- Fractional derivatives, New extended direct algebraic method, The ion sound as well as Langmuir waves, Traveling wave solutions,
- Publikační typ
- časopisecké články MeSH
Stratified flows are commonly observed in numerous industrial processes. For example, a gas-condensate pipeline typically uses a stratified flow regime. However, this flow arrangement is stable only under a specific set of operating conditions that allows the formation of stratification. In this study, the authors analyzed the flow attributes of Prandtl Eyring liquid past an inclined sheet immersed in a stratified medium. The flow also characterizes the features of the magnetic field along with a first-order chemical reaction. Convective boundary constraints associated with the thermosolutal exchange at the extremity of the domain are also prescribed. The fundamental equations of the study are formulated in dimensional PDEs and converted into dimensionless ODEs via similar variables. The numerical solution of the modelled setup is acquired by executing computations using shooting and RK-4 methods. The intelligent computing paradigm working on the mechanism of the back-propagated Levenberg-Marquardt strategy is also capitalized to forecast the behavior of related physical quantities. Graphs and tables are drawn to elaborate the impression of pertinent factors on flow distributions. It is perceived that the momentum profile diminishes with the magnetic field effect, whereas the opposite behavior is observed for the skin friction coefficient. The thermal and concentration distributions were found to dominate in the absence of stratification. Consideration of convective heating and concentration tends to elevate thermal and mass distributions.
- Klíčová slova
- Artificial neural networking, Chemical reaction, Convective boundary constraints, MHD, Prandtl-Eyring fluid, Thermosolutal stratification,
- Publikační typ
- časopisecké články MeSH
This study introduces an advanced approach for ranking international football players, addressing the inherent uncertainties in performance evaluations. By integrating dual possibility theory and Pythagorean fuzzy sets, the model accommodates varying degrees of ambiguity and imprecision in player attributes. Additionally, the use of hypersoft set theory enriches the analysis by capturing the multifaceted nature of player evaluations. The proposed aggregation operators refine the synthesis of diverse information sources, leading to a comprehensive and nuanced assessment. This research significantly enhances player evaluation methodologies, providing a more adaptable framework for a fair assessment of international football talent. A practical example illustrates the application of dual-possibility Pythagorean fuzzy hypersoft sets (DP-PFHSS). A numerical technique is proposed for solving multi-criteria decision-making (MCDM) challenges with known dual possibility information using the proposed aggregation operators. This decision-making algorithm effectively determines a football player's worth, contributing to the overall ranking and evaluation process. The approach aids in scouting and recruitment by facilitating talent identification and informed player signings. Graphical analysis, comparing existing and proposed methods using average and geometric operators, demonstrates the superiority of the proposed approach in the players evaluation, indicating that F 1 is in the top ranking.
- Klíčová slova
- Comparison, Dual possibility, Hypersoft set, Pythagorean fuzzy soft set, Ranking and decision making,
- Publikační typ
- časopisecké články MeSH
This manuscript contains several new spaces as the generalizations of fuzzy triple controlled metric space, fuzzy controlled hexagonal metric space, fuzzy pentagonal controlled metric space and intuitionistic fuzzy double controlled metric space. We prove the Banach fixed point theorem in the context of intuitionistic fuzzy pentagonal controlled metric space, which generalizes the previous ones in the existing literature. Further, we provide several non-trivial examples to support the main results. The capacity of intuitionistic fuzzy pentagonal controlled metric spaces to model hesitation, capture dual information, handle imperfect information, and provide a more nuanced representation of uncertainty makes them important in dynamic market equilibrium. In the context of changing market dynamics, these aspects contribute to a more realistic and flexible modelling approach. We present an application to dynamic market equilibrium and solve a boundary value problem for a satellite web coupling.
- MeSH
- algoritmy MeSH
- fuzzy logika * MeSH
- internet MeSH
- lidé MeSH
- teoretické modely MeSH
- Check Tag
- lidé MeSH
- Publikační typ
- časopisecké články MeSH
This article aims to study the time fractional coupled nonlinear Schrödinger equation, which explains the interaction between modes in nonlinear optics and Bose-Einstein condensation. The proposed generalized projective Riccati equation method and modified auxiliary equation method extract a more efficient and broad range of soliton solutions. These include novel solutions like a combined dark-lump wave soliton, multiple dark-lump wave soliton, two dark-kink solitons, flat kink-lump wave, multiple U-shaped with lump wave, combined bright-dark with high amplitude lump wave, bright-dark with lump wave and kink dark-periodic solitons are derived. The travelling wave patterns of the model are graphically presented with suitable parameters in 3D, density, contour and 2D surfaces, enhancing understanding of parameter impact. The proposed model's dynamics were observed and presented as quasi-periodic chaotic, periodic systems and quasi-periodic. This analysis confirms the effectiveness and reliability of the method employed, demonstrating its applicability in discovering travelling wave solitons for a wide range of nonlinear evolution equations.
- MeSH
- algoritmy MeSH
- nelineární dynamika * MeSH
- teoretické modely MeSH
- Publikační typ
- časopisecké články MeSH
This study endeavors to examine the dynamics of the generalized Kadomtsev-Petviashvili (gKP) equation in (n + 1) dimensions. Based on the comprehensive three-wave methodology and the Hirota's bilinear technique, the gKP equation is meticulously examined. By means of symbolic computation, a number of three-wave solutions are derived. Applying the Lie symmetry approach to the governing equation enables the determination of symmetry reduction, which aids in the reduction of the dimensionality of the said equation. Using symmetry reduction, we obtain the second order differential equation. By means of applying symmetry reduction, the second order differential equation is derived. The second order differential equation undergoes Galilean transformation to obtain a system of first order differential equations. The present study presents an analysis of bifurcation and sensitivity for a given dynamical system. Additionally, when an external force impacts the underlying dynamic system, its behavior resembles quasi-periodic phenomena. The presence of quasi-periodic patterns are identified using chaos detecting tools. These findings represent a novel contribution to the studied equation and significantly advance our understanding of dynamics in nonlinear wave models.
- MeSH
- algoritmy MeSH
- nelineární dynamika * MeSH
- teoretické modely MeSH
- Publikační typ
- časopisecké články MeSH
