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A Fractional Order Covid-19 Epidemic Model with Mittag–Leffler Kernel

Journal of Mathematical Sciences (United States) 2023年第2期272卷 284-306页

作者： Khan, H. Ibrahim, M. Khan, A. Tunç, O. Abdeljawad, Th. Department of Mathematics Shaheed Benazir Bhutto University Sheringal District Dir(Upper) Khyber Pakhtunkhwa Pakistan Department of Mathematics and General Science Prince Sultan University Riyadh 11586 Saudi Arabia Department of Computer Programing Baskale Vocational School Van Yuzuncu Yil University Van Turkey Department of Medical Research China Medical University Taichung Taiwan Department of Computer Science and Information Engineering Asia University Taichung Taiwan

We consider a nonlinear fractional-order Covid-19 model in a sense of the Atagana–Baleanu fractional derivative used for the analytic and computational studies. The model consists of six classes of persons, including susceptible, protected susceptible, asymptomatic infected, symptomatic infected, quarantined, and recovered individuals. The model is studied for the existence of solution with the help of a successive iterative technique with limit point as the solution of the model. The Hyers–Ulam stability is also studied. A numerical scheme is proposed and tested on the basis of the available literature. The graphical results predict the curtail of spread within the next 5000 days. Moreover, there is a gradual increase in the population of protected susceptible individuals. © 2023, Springer Nature Switzerland AG.

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Thermal and Flow Properties of Jeffrey Fluid Through Prabhakar Fractional Approach: Investigating Heat and Mass Transfer with Emphasis on Special Functions

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International Journal of Applied and Computational Mathematics 2024年第3期10卷 1-21页

作者： Riaz, Muhammad Bilal Rehman, Aziz Ur Chan, Choon Kit Zafar, Azhar Ali Tunç, Osman IT4Innovations VSB – Technical University of Ostrava Ostrava Czech Republic Department of Computer Science and Mathematics Lebanese American University Byblos Lebanon Faculty of Engineering and Quantity Surveying INTI International University Negeri Sembilan Putra Nilai 71800 Malaysia Department of Mathematics University of Management and Technology Lahore Lahore Pakistan Department of Mathematics Government College University Lahore Lahore Pakistan Department of Computer Programing Baskale Vocational School Van Yuzuncu Yil University Campus Van 65080 Turkey

The core purpose of this work is the investigation, formulation and develop a mathematical model by dint of a new fractional modeling approach namely Prabhakar fractional operator to study the dynamics of Jeffrey fluid flow and heat transfer phenomena. Exact analysis of natural convective flow of the Jeffrey fluid to derive analytical solutions with the non-integer order derivative Prabhakar fractional operator with non-singular type kernel alongwith application of generalized laws namely Fick’s and Fourier’s are reported here. This fractional operator has multi parameter generalized Mittag-Leffler kernel. The fluid flow is elaborated near an infinitely vertical plate with characteristics velocity u₀. The modeling of the considered problem is done in terms of the partial differential equations together with generalized boundary conditions. Introduced the appropriate set of variables to transform the governing equations into dimensionless form. Laplace transform is operated on the fractional system of equations and results are presented in series form and also presented the solution in the form of special functions. The pertinent parameter’s influence such as α, Pr, β, Gm, Sc, γ, Gr on the fluid flow is brought under consideration to reveal the interesting results. In comparison, we noticed the Prabhakar-like non integer approach shows better results than the existing operators in the literature, and graphs are drawn to show the results. Also, obtained the results in a limiting sense such as second grade fluid, Newtonian fluid in fractionalized form as well as Jeffrey and viscous fluid models for classical form from Prabhakar-like non integer Jeffrey fluid model. © The Author(s), under exclusive licence to Springer Nature India Private Limited 2024.

关键词： Analytical solution Heat transfer Laplace transformation Physical parameters Porous medium Prabhakar derivative Special functions

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Fractional dynamics and sensitivity analysis of measles epidemic model through vaccination

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Arab Journal of Basic and Applied Sciences 2024年第1期31卷 265-281页

作者： Riaz, Muhammad Bilal Raza, Nauman Martinovic, Jan Bakar, Abu Kurkcu, Harun Tunç, Osman IT4Innovations VSB–Technical University of Ostrava Ostrava Czech Republic Department of Computer Science and Mathematics Lebanese American University Byblos Lebanon Department of Mathematics University of the Punjab Lahore Pakistan Department of Mathematics Near East University TRNC Nicosia Turkey Department of Medicine and Surgery Research Centre on Public Health (CESP) University of Milano-Biccoca Monza Italy Department of Mathematics and Natural Sciences Gulf University for Science and Technology Mubarak Al-Abdullah Kuwait Department of Computer Programing Baskale Vocational School Van Yuzuncu Yil University Van Turkey

Measles is a highly contagious disease that mainly affects children worldwide. Even though a reliable and effective vaccination is available, there were 140,000 measles deaths worldwide in 2018, and most of them were children under the age five years. In this paper, we comprehensively investigate a novel fractional SVEIR (Susceptible-Vaccinated-Exposed-Infected-Recovered) model of the measles epidemic powered by nonlinear fractional differential equations to understand the epidemic’s dynamical behaviour. We use a non-singular Atangana-Baleanu fractional derivative to analyze the proposed model, taking advantage of non-locality. The existence, uniqueness, positivity and boundedness of the solutions are shown via concepts of fixed point theory, and we also perform the Ulam-Hyers stability of the considered model. The parameter sensitivity is discussed in the context of the variance with each parameter using 3-D graphics based on the basic reproduction number. Moreover, with the Atangana-Toufik numerical scheme, numerical findings are depicted for different fractional-order values. The presented approach produce results that are efficiently consistent and in excellent agreement with the theoretical results. © 2024 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group on behalf of the University of Bahrain.

关键词： Atangana-Baleanu derivative measles numerical analysis sensitivity analysis Ulam-Hyers stability

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Battle royale optimizer with a new movement strategy

arXiv

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arXiv 2022年

作者： Akan, Sara Akan, Taymaz Department of Computer Programing Ayvansaray University Istanbul Turkey Department of Software Engineering Ayvansaray University Istanbul Turkey

Gamed-based is a new stochastic metaheuristics optimization category that is inspired by traditional or digital game genres. Unlike SI-based algorithms, individuals do not work together with the goal of defeating other individuals and winning the game. Battle royale optimizer (BRO) is a Gamed-based metaheuristic optimization algorithm that has been recently proposed for the task of continuous problems. This paper proposes a modified BRO (M-BRO) in order to improve balance between exploration and exploitation. For this matter, an additional movement operator has been used in the movement strategy. Moreover, no extra parameters are required for the proposed approach. Furthermore, the complexity of this modified algorithm is the same as the original one. Experiments are performed on a set of 19 (unimodal and multimodal) benchmark functions (CEC 2010). The proposed method has been compared with the original BRO alongside six well-known/recently proposed optimization algorithms. The results show that BRO with additional movement operator performs well to solve complex numerical optimization problems compared to the original BRO and other competitors. Copyright © 2022, The Authors. All rights reserved.

关键词： Optimization

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The Data Dissemination Planning Tasks Process Model Into Account the Entities Differentity

The Data Dissemination Planning Tasks Process Model Into Acc...

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IEEE International Conference on Dependable Systems, Services and Technologies (DESSERT)

作者： Serhii Semenov Viacheslav Lymarenko Serhii Yenhalychev Svitlana Gavrilenko Cybersecurity and Information Technologies Department Simon Kuznets Kharkiv National University of Economics Kharkiv Ukraine The Computer Engineering and Programing Department National Technical University “Kharkiv Polytechnic Institute” Kharkiv Ukraine

ISBN: (纸本)9798350333053

The document presents a model for the planning process for data dissemination tasks. A distinctive feature of the model is that it takes into account the heterogeneity of entities by including additional blocks for their analysis and adaptation to the existing capabilities of processor and other resources. In the course of modeling, a classification was given to the concept of “entities”, a block diagram of the flow of entities for planning systems was developed and investigated. A generalized model for scheduling tasks and entities with dependencies has also been developed. The simulation was carried out using the GERT-network technology. As a result, GERT-networks of the process of scheduling distribution tasks for a separate n-th set of data type are obtained. The simulation result is presented in the form of an analytical expression for calculating the scheduling time for data dissemination tasks, taking into account the heterogeneity of entities.

关键词： Adaptation models Analytical models Processor scheduling Computational modeling Simulation Data dissemination Data models

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Signature of conservation laws and solitary wave solution with different dynamics in Thomas–Fermi plasma: Lie theory

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Partial Differential Equations in Applied Mathematics 2024年 12卷

作者： Fayyaz, Marriam Riaz, Muhammad Bilal Rehman, Muhammad Junaid U Tunç, Osman Department of Mathematics University of Management and Technology Lahore Pakistan IT4Innovations VSB – Technical University of Ostrava Ostrava Czech Republic Department of Computer Science and Mathematics Lebanese American University Byblos Lebanon Department of Mathematics Quaid-I-Azam University Islamabad 45320 Pakistan Department of Computer Programing Baskale Vocational School Van Yuzuncu Yil University Van Campus 65080 Turkey

We propose a Lie group method to discuss the modified KP equation appearing in Thomas–Fermi (TM) plasma, characterised by cold and hot electrons. The Lie method facilitates the identification of similarity reductions, infinitesimal symmetries, group-invariant solutions, and novel analytical solutions for nonlinear models. The similarity reduction method is carried out to transform the nonlinear partial differential equations (NLPDE) into the nonlinear ordinary differential equations (NLODE). This study focuses on solitary wave profiles due to their usefulness in various engineering applications, including monitoring public transportation systems, managing coastlines, and mitigating disaster risks. It also addresses the conservation laws associated with the modified KP equation. The generalised auxiliary equation (GAEM) scheme is used to compute the new solitary wave patterns of the modified KP equation, which explains the dynamics of nonlinear waves in Thomas–Fermi plasma. The idea of nonlinear self-adjointness is used to compute the conservation laws of the examined model. The graphical behaviour of some solutions is represented by adjusting the suitable value of the parameters involved. © 2024 The Authors

关键词： Conservation laws Generalised auxiliary equation method Lie theory Modified KP equation Solitary wave solutions

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Correction to: A Fractional Order Covid-19 Epidemic Model with Mittag-Leffler Kernel

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Journal of Mathematical Sciences 2023年第2期273卷 332-332页

作者： Khan, H. Ibrahim, M. Khan, A. Tunç, O. Abdeljawad, Th. Department of Mathematics Shaheed Benazir Bhutto University District Dir(Upper) Pakistan Department of Mathematics and Sciences Prince Sultan University Riyadh Saudi Arabia Department of Computer Programing Baskale Vocational School Van Yuzuncu Yil University Van Turkey

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Hybrid Data Set Optimization in Recommender Systems Using Fuzzy T-Norms 1

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15th IFIP WG 12.5 International Conference on Artificial Intelligence Applications and Innovations, AIAI 2019

作者： Papaleonidas, Antonios Pimenidis, Elias Iliadis, Lazaros School of Engineering Department of Civil Engineering Faculty of Mathematics Programing and General Courses Democritus University of Thrace Kimmeria Xanthi Greece Department of Computer Science and Creative Technologies University of the West of England BristolBS16 1QY United Kingdom

ISBN: (数字)9783030198237

ISBN: (纸本)9783030198220

A recommender system uses specific algorithms and techniques in order to suggest specific services, goods or other type of recommendations that users could be interested in. User’s preferences or ratings are used as inputs and top-N recommendations are produced by the system. The evaluation of the recommendations is usually based on accuracy metrics such as the Mean Absolute Error (MAE) and the Root Mean Squared Error (RMSE), while on the other hand Precision and Recall is used to measure the quality of the top-N recommendations. Recommender systems development has been mainly focused in the development of new recommendation algorithms. However, one of the major problems in modern offline recommendation system is the sparsity of the datasets and the selection of the suitable users Y that could produce the best recommendations for users X. In this paper, we propose an algorithm that uses Fuzzy sets and Fuzzy norms in order to evaluate the correlation between users in the data set so the system can select and use only the most relevant users. At the same time, we are extending our previous work about Reproduction of experiments in recommender systems by developing new explanations and variables for the proposed new algorithm. Our proposed approach has been experimentally evaluated using a real dataset and the results show that it is really efficient and it can increase both accuracy and quality of recommendations. © 2019, IFIP International Federation for Information Processing.

关键词： Fuzzy logic

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Prediction of surface roughness using artificial neural network in lathe 08

Prediction of surface roughness using artificial neural netw...

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9th International Conference on computer Systems and Technologies and Workshop for PhD Students in Computing, CompSysTech'08

作者： Tasdemir, Sakir Neseli, Süleyman Saritas, Ismail Yaldiz, Süleyman Department of Computer Technology and Programing Technical Science College Selcuk University Konya Turkey Department of Mechanical Technology Technical Science College Selcuk University Konya Turkey Department of Electronic and Computur Education Technical Education Faculty Selcuk University Konya Turkey

ISBN: (纸本)9789549641523

In this study, the effect of tool geometry on surface roughness has been investigated in universal lathe. Machining process has been carried out on AISI 1040 steel in dry cutting condition using various insert geometry at depth of cut off 0.5 mm. At the end of the cutting operation, surface roughness has been measured using MAHR M1 perthometer. After experimental study, to predict the surface roughness, an ANN has been modelled using the data obtained. Modelling of ANN;tool nose radius (r), approach angle (K), rake angle (Y), tool overhang (L) have been used. In this study, surface roughness (Ra) is output data. The ANN has been designed on PC by using Matlab 6.5 software. Comparison of the experimental data and ANN results by means of statistically t test show that there is no significant difference and ANN has been used confidently.

关键词： Surface roughness

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