WoS İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653
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Article Citation - WoS: 9Citation - Scopus: 11Monkeypox Viral Transmission Dynamics and Fractional-Order Modeling With Vaccination Intervention(World Scientific Publ Co Pte Ltd, 2023) Kumar, Sachin; Baleanu, Dumitru; Nisar, Kottakkaran sooppy; Singh, Jaskirat palA current outbreak of the monkeypox viral infection, which started in Nigeria, has spread to other areas of the globe. This affects over 28 nations, including the United Kingdom and the United States. The monkeypox virus causes monkeypox (MPX), which is comparable to smallpox and cowpox (MPXV). The monkeypox virus is a member of the Poxviridae family and belongs to the Orthopoxvirus genus. In this work, a novel fractional model for Monkeypox based on the Caputo derivative is explored. For the model, two equilibria have been established: disease-free and endemic equilibrium. Using the next-generation matrix and Castillo's technique, if R-0 < 1 the global asymptotic stability of disease-free equilibrium is shown. The linearization demonstrated that the endemic equilibrium point is locally asymptotically stable if R-0 > 1. Using the parameter values, the model's fundamental reproduction rates for both humans and non-humans are calculated. The existence and uniqueness of the solution are proved using fixed point theory. The model's numerical simulations demonstrate that the recommended actions will cause the infected people in the human and non-human populations to disappear.Article Citation - WoS: 3Citation - Scopus: 3On Ritz Approximation for a Class of Fractional Optimal Control Problems(World Scientific Publ Co Pte Ltd, 2022) Jafari, Hossein; Johnston, Sarah Jane; Baleanu, Dumitru; Firoozjaee, Mohammad ArabWe apply the Ritz method to approximate the solution of optimal control problems through the use of polynomials. The constraints of the problem take the form of differential equations of fractional order accompanied by the boundary and initial conditions. The ultimate goal of the algorithm is to set up a system of equations whose number matches the unknowns. Computing the unknowns enables us to approximate the solution of the objective function in the form of polynomials.Article Citation - WoS: 1Citation - Scopus: 1Mellin Transform for Fractional Integrals With General Analytic Kernel(Amer inst Mathematical Sciences-aims, 2022) Kalsoom, Amna; Sager, Maria; Inc, Mustafa; Baleanu, Dumitru; Alshomrani, Ali S.; Rashid, MalihaMany different operators of fractional calculus have been proposed, which can be organized in some general classes of operators. According to this study, the class of fractional integrals and derivatives can be classified into two main categories, that is, with and without general analytical kernel (introduced in 2019). In this article, we define the Mellin transform for fractional differential operator with general analytic kernel in both Riemann-Liouville and Caputo derivatives of order sigma >= 0 and. be a fixed parameter. We will also establish relation between Mellin transform with Laplace and Fourier transforms.Article Citation - WoS: 4Citation - Scopus: 4A Novel Formulation of the Fuzzy Hybrid Transform for Dealing Nonlinear Partial Differential Equations Via Fuzzy Fractional Derivative Involving General Order(Amer inst Mathematical Sciences-aims, 2022) Rashid, Saima; Kanwal, Bushra; Jarad, Fahd; Elagan, S. K.; Alqurashi, M. S.The main objective of the investigation is to broaden the description of Caputo fractional derivatives (in short, CFDs) (of order 0 < alpha < r) considering all relevant permutations of entities involving t(1) equal to 1 and t(2) (the others) equal to 2 via fuzz Under gH-differentiability, we also construct fuzzy Elzaki transforms for CFDs for the generic fractional order alpha is an element of (r - 1, r). Furthermore, a novel decomposition method for obtaining the solutions to nonlinear fuzzy fractional partial differential equations (PDEs) via the fuzzy Elzaki transform is constructed. The aforesaid scheme is a novel correlation of the fuzzy Elzaki transform and the Adorn ian decomposition method. In terms of CFD, several new results for the general fractional order are obtained via gH-differentiability. By considering the triangular fuzzy numbers of a nonlinear fuzzy fractional PDE, the correctness and capabilities of the proposed algorithm are demonstrated. In the domain of fractional sense, the schematic representation and tabulated outcomes indicate that the algorithm technique is precise and straightforward. Subsequently, future directions and concluding remarks are acted upon with the most focused use of references.Article Citation - WoS: 47Citation - Scopus: 52A Delayed Plant Disease Model With Caputo Fractional Derivatives(Springer, 2022) Baleanu, Dumitru; Erturk, Vedat Suat; Inc, Mustafa; Govindaraj, V; Kumar, PushpendraWe analyze a time-delay Caputo-type fractional mathematical model containing the infection rate of Beddington-DeAngelis functional response to study the structure of a vector-borne plant epidemic. We prove the unique global solution existence for the given delay mathematical model by using fixed point results. We use the Adams-Bashforth-Moulton P-C algorithm for solving the given dynamical model. We give a number of graphical interpretations of the proposed solution. A number of novel results are demonstrated from the given practical and theoretical observations. By using 3-D plots we observe the variations in the flatness of our plots when the fractional order varies. The role of time delay on the proposed plant disease dynamics and the effects of infection rate in the population of susceptible and infectious classes are investigated. The main motivation of this research study is examining the dynamics of the vector-borne epidemic in the sense of fractional derivatives under memory effects. This study is an example of how the fractional derivatives are useful in plant epidemiology. The application of Caputo derivative with equal dimensionality includes the memory in the model, which is the main novelty of this study.Article Citation - WoS: 4Citation - Scopus: 5Spectral Solutions for a Class of Nonlinear Wave Equations With Riesz Fractional Based on Legendre Collocation Technique(Elsevier, 2023) Abdelkawy, M. A.; Soluma, E. M.; Al-Dayel, Ibrahim; Baleanu, DumitruA numerical investigation is presented in this work for a class of Riesz space-fractional nonlinear wave equations (MD-RSFN-WEs). The presence of a spatial Laplacian of fractional order, stated by fractional Riesz derivatives, is taken into consideration by the model. The fractional wave equation governs mechanical diffusive wave propagation in viscoelastic medium with power-law creep and, as a result, gives a physical under-standing of this equation within the context of dynamic viscoelasticity. To deal with the independent variables, a totally spectral collocation approach is used. Our approach has shown to be more precise, efficient, and practical for the present model. The findings demonstrated that the spectral scheme is exponentially convergent.(c) 2022 Elsevier B.V. All rights reserved.Article Citation - WoS: 36Citation - Scopus: 36All Linear Fractional Derivatives With Power Functions' Convolution Kernel and Interpolation Properties(Pergamon-elsevier Science Ltd, 2023) Baleanu, Dumitru; Shiri, BabakOur attempt is an axiomatic approach to find all classes of possible definitions for fractional derivatives with three axioms. In this paper, we consider a special case of linear integro-differential operators with power functions' convolution kernel a(a)(t-s)b(a) of order a a (0,1). We determine analytic functions a(a) and b(a) such that when a-* 0+, the corresponding operator becomes identity operator, and when a-* 1- the corresponding operator becomes derivative operator. Then, a sequential operator is used to extend the fractional operator to a higher order. Some properties of the sequential operator in this regard also are studied. The singularity properties, Laplace transform and inverse of the new class of fractional derivatives are investigated. Several examples are provided to confirm theoretical achievements. Finally, the solution of the relaxation equation with diverse fractional derivatives is obtained and compared.Article Citation - WoS: 9Citation - Scopus: 11Time-Fractional Nonlinear Swift-Hohenberg Equation: Analysis and Numerical Simulation(Elsevier, 2020) Nasr, M. A.; Baleanu, Dumitru; Zahra, W. K.In this paper, a new scheme based on the exponential fitting technique is presented for solving the nonlinear time-fractional Swift-Hohenberg equation, where the first and second-order derivatives are replaced by Caputo fractional derivative. The exponential fitting technique depends on a parameter that led to getting high-order accuracy. The convergence and unconditional stability will be discussed using the Fourier method and the analysis is built on uniform and nonuniform time steps, to solve initial singularity by using the graded meshes. Applicability and theoretical results will be demonstrated and enhanced with numerical examples. (C) 2020 The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University.Article Citation - WoS: 32Citation - Scopus: 38On the Analysis of an Analytical Approach for Fractional Caudrey-Dodd Equations(Elsevier, 2022) Gupta, Arpita; Baleanu, Dumitru; Singh, JagdevThe principal aim of this paper is to study the approximate solution of nonlinear Caudrey-Dodd-Gibbon equation of fractional order by employing an analytical method. The Caudrey-Dodd-Gibbon equation arises in plasma physics and laser optics. The Caputo derivative is applied to model the physical problem. By applying an effective semi-analytical technique, we attain the approximate solutions without linearization. The uniqueness and the convergence analysis for the applied method are shown. The graphical representation of solutions of fractional Caudrey-Dodd-Gibbon equation demonstrates the applied technique is very efficient to obtain the solutions of such type of fractional order mathematical models. (c) 2021 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).Article Citation - WoS: 1Citation - Scopus: 1Numerical Solutions of Fuzzy Equal Width Models Via Generalized Fuzzy Fractional Derivative Operators(Amer inst Mathematical Sciences-aims, 2022) Rashid, Saima; Jarad, Fahd; Althobaiti, Ali; Ashraf, RehanaThe Shehu homotopy perturbation transform method (SHPTM) via fuzziness, which combines the homotopy perturbation method and the Shehu transform, is the subject of this article. With the assistance of fuzzy fractional Caputo and Atangana-Baleanu derivatives operators, the proposed methodology is designed to illustrate the reliability by finding fuzzy fractional equal width (EW), modified equal width (MEW) and variants of modified equal width (VMEW) models with fuzzy initial conditions (ICs). In cold plasma, the proposed model is vital for generating hydro-magnetic waves. We investigated SHPTM's potential to investigate fractional nonlinear systems and demonstrated its superiority over other numerical approaches that are accessible. Another significant aspect of this research is to look at two significant fuzzy fractional models with differing nonlinearities considering fuzzy set theory. Evaluating various implementations verifies the method's impact, capabilities, and practicality. The level impacts of the parameter h and fractional order are graphically and quantitatively presented, demonstrating good agreement between the fuzzy approximate upper and lower bound solutions. The findings are numerically examined to crisp solutions and those produced by other approaches, demonstrating that the proposed method is a handy and astonishingly efficient instrument for solving a wide range of physics and engineering problems.
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