Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
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Article Citation - WoS: 6Citation - Scopus: 6On Modeling the Groundwater Flow Within a Confined Aquifer(Editura Acad Romane, 2015) Atangana, Abdon; Baleanu, Dumitru; Baleanu, Dumitru; MatematikThe groundwater flow equation is used to simulate the movement of water under the confined aquifer. In this paper we study a modification of the groundwater flow equation within a newly proposed derivative. We numerically solve the generalized groundwater flow equation with the Crank-Nicholson scheme. We also analytically solve the generalized equation via the method of separation of variable.Article Citation - WoS: 69Citation - Scopus: 73Classical and Fractional Aspects of Two Coupled Pendulums(Editura Acad Romane, 2019) Baleanu, D.; Baleanu, Dumitru; Jajarmi, A.; Asad, J. H.; MatematikIn this study, we consider two coupled pendulums (attached together with a spring) having the same length while the same masses are attached at their ends. After setting the system in motion we construct the classical Lagrangian, and as a result, we obtain the classical Euler-Lagrange equation. Then, we generalize the classical Lagrangian in order to derive the fractional Euler-Lagrange equation in the sense of two different fractional operators. Finally, we provide the numerical solution of the latter equation for some fractional orders and initial conditions. The method we used is based on the Euler method to discretize the convolution integral. Numerical simulations show that the proposed approach is efficient and demonstrate new aspects of the real-world phenomena.Article Citation - WoS: 67Citation - Scopus: 69The Fractional Model of Spring Pendulum: New Features Within Different Kernels(Editura Acad Romane, 2018) Baleanu, Dumitru; Baleanu, Dumitru; Asad, Jihad H.; Jajarmi, Amin; MatematikIn this work, new aspects of the fractional calculus (FC) are examined for a model of spring pendulum in fractional sense. First, we obtain the classical Lagrangian of the model, and as a result, we derive the classical Euler-Lagrange equations of the motion. Second, we generalize the classical Lagrangian to fractional case and derive the fractional Euler-Lagrange equations in terms of fractional derivatives with singular and nonsingular kernels, respectively. Finally, we provide the numerical solution of these equations within two fractional operators for some fractional orders and initial conditions. Numerical simulations verify that taking into account the recently features of the FC provides more realistic models demonstrating hidden aspects of the real-world phenomena.Article Citation - WoS: 3Citation - Scopus: 4Numerical Analysis of Fractional Order Discrete Bloch Equa-Tions(int Scientific Research Publications, 2024) Santra, Shyam Sundar; Jayanathan, Leo Amalraj; Baleanu, Dumitru; Murugesan, MeganathanBy defining a new kind of h-extorial function with constant coefficient, this research seeks to solve discrete fractional Bloch equations. By using an extorial function of the Mittag-Leffler type, we are able to discover the general solutions for the magnetization's Bx, By, and Bz components. These findings demonstrate the innovative method of fractional order Bloch equations. In addition, we offer a graphical representation of our results.(c) 2024 All rights reserved.Article Citation - WoS: 15Citation - Scopus: 23Optical Solitons With Nonlinear Dispersion in Parabolic Law Medium and Three-Component Coupled Nonlinear Schrodinger Equation(Springer, 2022) Sulaiman, Tukur Abdulkadir; Alshomrani, Ali S.; Baleanu, Dumitru; Yusuf, AbdullahiThe current study looks at two different nonlinear Schrodinger equations. These equations have several applications in science and engineering, such as nonlinear fiber optics, electromagnetic field waves, and signal processing via optical fibers. In this study, we investigate these equations using an efficient integration strategy known as complex envelop antazs. As a result, we obtain novel solutions such as bright, dark, and combined dark-bright soliton solutions. Important physical aspects have been depicted in three dimensions and contour plots for clear interpretation of the acquired solutions.Article Citation - WoS: 132Citation - Scopus: 158On a New and Generalized Fractional Model for a Real Cholera Outbreak(Elsevier, 2022) Ghassabzade, Fahimeh Akhavan; Nieto, Juan J.; Jajarmi, Amin; Baleanu, DumitruIn this paper, a new mathematical model involving the general form of Caputo fractional derivative is studied for a real case of cholera outbreak. Fundamental properties of the new model including the equilibrium points as well as the basic reproduction number are explored. Also, an efficient approximation scheme on the basis of product-integration rule is established to solve the new model. Several kernel functions for the general fractional derivative are tested, and the results are compared with the real data of a cholera outbreak in Yemen. As a consequence, we find a special case in which the aforesaid outbreak is described better, for the corresponding numerical simulations are closer to the real data than the other classical and fractional frameworks. Next, we apply the most realistic model to investigate the effect of vaccination on the considered cholera outbreak. Simulation results show that earlier vaccination could reduce the number of infected individuals effectively, so mortality would have been reduced considerably if the vaccination had been performed earlier. (c) 2022 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: 111Citation - Scopus: 123Stability Analysis and System Properties of Nipah Virus Transmission: a Fractional Calculus Case Study(Pergamon-elsevier Science Ltd, 2023) Shekari, Parisa; Torkzadeh, Leila; Ranjbar, Hassan; Jajarmi, Amin; Nouri, Kazem; Baleanu, DumitruIn this paper, we establish a Caputo-type fractional model to study the Nipah virus transmission dynamics. The model describes the impact of unsafe contact with an infectious corpse as a possible way to transmit this virus. The corresponding area to the system properties, including the positivity and boundedness of the solution, is explored by using the generalized fractional mean value theorem. Also, we investigate sufficient conditions for the local and global stability of the disease-free and the endemic steady-states based on the basic reproduction number R0. To show these important stability features, we employ fractional Routh-Hurwitz criterion and LaSalle's invariability principle. For the implementation of this epidemic model, we also use the Adams-Bashforth-Moulton numerical method in a fractional sense. Finally, in addition to compare the fractional and classical results, as one of the main goals of this research, we demonstrate the usefulness of minimal unsafe touch with the infectious corpse. Simulation and comparative results verify the theoretical discussions.Article On Hilbert-Pachpatte Type Inequalities Within ?-Hilfer Fractional Generalized Derivatives(Amer inst Mathematical Sciences-aims, 2023) Baleanu, Dumitru; Basci, YaseminIn this manuscript, we discussed various new Hilbert-Pachpatte type inequalities implying the left sided psi-Hilfer fractional derivatives with the general kernel. Our results are a generalization of the inequalities of Pecaric ' and Vukovic ' [1]. Furthermore, using the specific cases of the psi-Hilfer fractional derivative, we proceed with wide class of fractional derivatives by selecting psi, a1, b1 and considering the limit of the parameters alpha and beta.Article Citation - WoS: 18Citation - Scopus: 20Comprehending the Model of Omicron Variant Using Fractional Derivatives(Taylor & Francis Ltd, 2023) Goswami, Pranay; Baleanu, Dumitru; Shankar Dubey, Ravi; Sharma, ShivaniThe world is grappled with an unprecedented challenges due to Corona virus. We are all battling this epidemic together, but we have not been able to defeat this epidemic yet. A new variant of this virus, named 'Omicron' is spreading these days. The fractional differential equations are providing us with better tools to study the mathematical model with memory effects. In this paper, we will consider an extended SER mathematical model with quarantined and vaccinated compartment to speculate the Omicron variant. This extended Susceptible Exposed Infected Recovered SER model involves equations that associate with the group of individuals those are susceptible (S), exposed (E): this class includes the individuals who are infected but not yet infectious, infectious (W): this class includes the individuals who are infected but not yet Quarantined, quarantined (Q): this class includes those group of people who are infectious, confirmed and quarantined, recovered (R) this class includes the group of individuals who have recovered, and vaccinated (V): this class includes the group of individuals who have been vaccinated. The non-negativity and of the extended SER model is analysed, the equilibrium points and the basic reproduction number are also calculated. The proposed model is then extended to the mathematical model using AB derivative operator. Proof for the existence and the uniqueness for the solution of fractional mathematical model in sense of AB fractional derivative is detailed and a numerical method is detailed to obtain the numerical solutions. Further we have discussed the efficiency of the vaccine against the Omicron variant via graphical representation.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.