Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
Browse
129 results
Search Results
Article Optimal Control for a Variable-Order Diffusion-Wave Equation With a Reaction Term; a Numerical Study(Elsevier B.V., 2024) Megahed, F.; Shatta, S.A.; Baleanu, D.; Sweilam, N.H.In this paper, optimal control for a variable-order diffusion-wave equation with a reaction term is numerically studied, where the variable-order operator is defined in the sense of Caputo proportional constant. Necessary optimality conditions for the control problem are derived. Existence and uniqueness for the solutions of fractional optimal control problem are derived. The nonstandard weighted average finite difference method and the nonstandard leap-frog method are developed to study numerically the proposed problem. Moreover, the stability analysis of the methods is proved. Finally, in order to characterise the memory property of the proposed model, three test examples are given. It is found that the nonstandard weighted average finite difference method can be applied to study such variable-order fractional optimal control problems simply and effectively. © 2024 The Author(s)Article Citation - Scopus: 7Heuristic Computing With Active Set Method for the Nonlinear Rabinovich–fabrikant Model(Elsevier Ltd, 2023) Baleanu, D.; E Alhazmi, S.; Ben Said, S.; Sabir, Z.The current study shows a reliable stochastic computing heuristic approach for solving the nonlinear Rabinovich-Fabrikant model. This nonlinear model contains three ordinary differential equations. The process of stochastic computing artificial neural networks (ANNs) has been applied along with the competences of global heuristic genetic algorithm (GA) and local search active set (AS) methodologies, i.e., ANNs-GAAS. The construction of merit function is performed through the differential Rabinovich-Fabrikant model. The results obtained through this scheme are simple, reliable, and accurate, which have been calculated to optimize the merit function by using the GAAS method. The comparison of the obtained results through this scheme and the conventional reference solutions strengthens the correctness of the proposed method. Ten numbers of neurons along with the log-sigmoid transfer function in the neural network structure have been used to solve the model. The values of the absolute error are performed around 10−07 and 10−08 for each class of the Rabinovich-Fabrikant model. Moreover, the reliability of the ANNs-GAAS approach is observed by using different statistical approaches for solving the Rabinovich-Fabrikant model. © 2023 The AuthorsArticle Citation - Scopus: 14A Fractional Order Co-Infection Model Between Malaria and Filariasis Epidemic(Taylor and Francis Ltd., 2024) Kumar, A.; Kumar, S.; Baleanu, D.; Kumar, P.In this article, we investigate a mathematical malaria-filariasis co-infection model with the assistance of the non-integer order operator. Using the fractal-fractional operator in the Caputo-Fabrizio (CF) sense, it has been possible to understand the dynamical behaviour and complicatedness of the malaria-filariasis model. An investigation of the existence and uniqueness of the solution employs fixed-point theory. Ulam-Hyers stability helps examine the stability analysis of the proposed co-infection model. The malaria-filariasis model has been investigated using the Toufik-Atanagana (TA), a sophisticated numerical method for these biological co-infection models. With the help of numerical procedures, we provide the approximate solutions for the proposed model. A variety of fractal dimension and fractional order options are utilized for the presentation of the results. When we adjust sensitive parameters like τ and γ, the graphical representation illustrates the system’s behaviour and identifies suitable parameter ranges for solutions. In addition, we evaluate the model along with the regarded operators and various β1 values using an exceptional graphical representation. © 2024 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group on behalf of the University of Bahrain.Article Citation - Scopus: 10Third-Order Neutral Differential Equations of the Mixed Type: Oscillatory and Asymptotic Behavior(American Institute of Mathematical Sciences, 2022) Qaraad, B.; Moaaz, O.; Baleanu, D.; Santra, S.S.; Ali, R.; Elabbasy, E.M.In this work, by using both the comparison technique with first-order differential inequalities and the Riccati transformation, we extend this development to a class of third-order neutral differential equations of the mixed type. We present new criteria for oscillation of all solutions, which improve and extend some existing ones in the literature. In addition, we provide an example to illustrate our results. © 2022 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)Article Citation - Scopus: 26Search for Adequate Closed Form Wave Solutions To Space–time Fractional Nonlinear Equations(Elsevier B.V., 2021) Akbar, M.A.; Seadawy, A.R.; Baleanu, D.; Roy, R.The nonlinear space–time fractional Phi-4 equation and density dependent fractional reaction–diffusion equation (FRDE) are important models to interpret the fusion and fission phenomena ensued in solid state physics, plasma physics, chemical kinematics, astrophysical fusion plasma, electromagnetic interactions etc. In this study, we search advanced and wide-ranging wave solutions to the formerly reported nonlinear fractional evolution equations in diverse family through the new generalized (G′∕G)-expansion technique. The solutions are developed with trigonometric, hyperbolic, exponential and rational functions including parameters. The technique is a compatible, functional and effective scientific scheme to examine diverse space–time fractional models in physics and engineering concerned with the real life problems. © 2021 The AuthorsEditorial Citation - Scopus: 1New Trends on Fractional and Functional Differential Equations(Hindawi Publishing Corporation, 2015) Bhrawy, A.H.; Van Gorder, R.A.; Baleanu, D.Article Citation - Scopus: 10The Korteweg-De Vries–caudrey–dodd–gibbon Dynamical Model: Its Conservation Laws, Solitons, and Complexiton(Shanghai Jiaotong University, 2022) Hosseini, K.; Akbulut, A.; Baleanu, D.; Salahshour, S.; Mirzazadeh, M.; Dehingia, K.The main purpose of the present paper is to conduct a detailed and thorough study on the Korteweg-de Vries–Caudrey–Dodd–Gibbon (KdV-CDG) dynamical model. More precisely, after considering the integrable KdV-CDG dynamical model describing certain properties of ocean dynamics, its conservation laws, solitons, and complexiton are respectively derived using the Ibragimov, Kudryashov, and Hirota methods. Several numerical simulations in two and three-dimensional postures are formally given to analyze the effect of nonlinear parameters. It is shown that nonlinear parameters play a key role in the dynamical properties of soliton and complexiton solutions. © 2022Article Citation - Scopus: 11Oscillation Result for Half-Linear Delay Di Erence Equations of Second-Order(American Institute of Mathematical Sciences, 2022) Santra, S.S.; Baleanu, D.; Edwan, R.; Govindan, V.; Murugesan, A.; Altanji, M.; Jayakumar, C.In this paper, we obtain the new single-condition criteria for the oscillation of secondorder half-linear delay difference equation. Even in the linear case, the sharp result is new and, to our knowledge, improves all previous results. Furthermore, our method has the advantage of being simple to prove, as it relies just on sequentially improved monotonicities of a positive solution. Examples are provided to illustrate our results. © 2022 the Author(s), licensee AIMS Press.Article Citation - Scopus: 12Optimal System and Symmetry Reduction of the (1+1) Dimensional Sawada-Kotera Equation(Academic Press, 2016) Kadkhoda, N.; Jafari, H.; Moremedi, G.M.; Baleanu, D.We study the nonlinear fifth order (1 + 1) dimensional Sawada-Kotera equation using Lie symmetry group. For this equation Lie point symmetry operators and optimal system are obtained. We determine the corresponding invariant solutions and reduced equations using obtained infinitesimal generators. © 2016 Academic Publications, Ltd.Article Citation - WoS: 12Citation - Scopus: 13Optical Solitons To the Ginzburg-Landau Equation Including the Parabolic Nonlinearity(Springer, 2022) Hosseini, K.; Mirzazadeh, M.; Akinyemi, L.; Baleanu, D.; Salahshour, S.The major goal of the present paper is to construct optical solitons of the Ginzburg-Landau equation including the parabolic nonlinearity. Such an ultimate goal is formally achieved with the aid of symbolic computation, a complex transformation, and Kudryashov and exponential methods. Several numerical simulations are given to explore the influence of the coefficients of nonlinear terms on the dynamical features of the obtained optical solitons. To the best of the authors' knowledge, the results reported in the current study, classified as bright and kink solitons, have a significant role in completing studies on the Ginzburg-Landau equation including the parabolic nonlinearity.