Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
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Article Citation - WoS: 46Citation - Scopus: 48Solutions of the Fractional Davey-Stewartson Equations With Variational Iteration Method(Editura Acad Romane, 2012) Baleanu, Dumitru; Jafari, Hossain; Kadem, Abdelouahab; Yılmaz, Tuğba; Baleanu, Dumitru; Yilmaz, Tugba; Matematik; PsikolojiThis paper presents approximate analytical solutions for the fractional Davey-Stewartson equations using the Variational iteration method. The fractional derivatives are described in the Caputo sense. This method is based on the incorporation of the correction functional for the equation. The results obtained by this method have been compared with the exact solutions and show that the introduced approach is a promising tool for solving many linear and nonlinear fractional differential equations.Article Citation - WoS: 11Numerical and Bifurcations Analysis for Multi Order Fractional Model of Hiv Infection of Cd4+t-cells(Univ Politehnica Bucharest, Sci Bull, 2016) Alipour, Mohsen; Baleanu, Dumitru; Arshad, Sadia; Baleanu, Dumitru; MatematikIn this paper, we solve the dynamical system of HIV infection of CD4(+) T cells within the multi-order fractional derivatives. The Bernstein operational matrices in arbitrary interval [a,b] are applied to obtain the approximate analytical solution of the model. In this way, the fractional differential equations are reduced to an algebraic easily solvable system. The obtained solutions are accurate and the method is very efficient and simple in implementation. With the help of bifurcation analysis, we acquired the critical value of viral death rate, that is, if viral death rate is greater than the critical value then level of virus particles starts to decline and thus free virus will eventually eliminate and patient is cured. Further, we found the threshold for viral infection rate analytically, which assures the stability of uninfected equilibrium and virus will ultimately eradicate.Article Citation - WoS: 52Citation - Scopus: 54Fractional Caputo Heat Equation Within the Double Laplace Transform(Editura Acad Romane, 2013) Jarad, Fahd; Anwar, A. M. O.; Jarad, Fahd; Baleanu, Dumitru; Baleanu, D.; Ayaz, F.; MatematikThe heat equation and its fractional generalization are used in various applications in science and engineering. In this paper firstly we introduce the double Laplace transform of the partial fractional integrals and derivatives which can be used to solve partial differential equations with Caputo fractional derivatives. Secondly, the fractional heat equation was investigated in details with the help of this new generalized transformArticle Citation - WoS: 6Citation - Scopus: 8The Role of Obesity in Fractional Order Tumor-Immune Model(Univ Politehnica Bucharest, Sci Bull, 2020) Arshad, Sadia; Baleanu, Dumitru; Yildiz, Tugba Akman; Baleanu, Dumitru; Tang, Yifa; MatematikThis work investigates the tumor-obesity model via a fractional operator to analyze the interactions between cancer and obesity, since fractional derivatives capture the long formation of cancerous tumor cells that might takes years to develop. It is known that fat cells enhance the development of cancerous tumor cells. To examine how the immune system is influenced due to fat cells, interactions of four types of cell population, namely tumor cells, immune cells, normal cells and fat cells are examined. We investigate the equilibrium points and discuss their stability analytically. Numerical simulations are carried out to verify the analytical results, demonstrating that a low fat diet results in a smaller tumor burden as compared to a high-caloric diet.Article Citation - WoS: 22Citation - Scopus: 28Non-Instantaneous Impulsive Fractional Integro-Differential Equations With State-Dependent Delay Br(Univ Maragheh, 2022) Salim, Abdelkrim; Aissani, Khalida; Benchohra, Mouffak; Karapinar, Erdal; Benkhettou, NadiaThis paper deals with the existence and uniqueness of the mild solution of the fractional integro-differential equations with non-instantaneous impulses and state-dependent delay. Our arguments are based on the fixed point theory. Finally, an example to confirm of the results is provided.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 - Scopus: 4Two Novel Methods for Fractional Nonlinear Whitham–broer–kaup Equations Arising in Shallow Water(Springer, 2023) Verma, V.; Baleanu, D.; Prakash, A.In the present paper, we investigate the approximate analytic solution of the time-fractional nonlinear coupled Whitham–Broer–Kaup equations arising in shallow water with the aid of two novel approaches namely q -homotopy analysis Sumudu transform method (q-HASTM) and Homotopy perturbation Sumudu transform method (HPSTM). Uniqueness and convergence analysis of the coupled WBK equations via q-HASTM are accessible. We applied the suggested techniques to a pair of examples, plotted the results and analyse the error, L2 error norm and L∞ error norm with q-HASTM and HPSTM. © 2023, The Author(s), under exclusive licence to Springer Nature India Private Limited.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: 5Citation - Scopus: 5Numerical Simulation for Time-Fractional Nonlinear Reaction-Diffusion System on a Uniform and Nonuniform Time Stepping(Wiley, 2021) Hikal, Manal M.; Baleanu, Dumitru; Zahra, Waheed K.In this article, two nonstandard high-order schemes on a uniform and nonuniform time stepping combined with the multi-parameter exponential fitting technique (MPEF) have been developed to solve the time-fractional nonlinear reaction-diffusion system. The first method based on the MPEF combined with the 3-weighted shifted-Grunwald-Letnikov approximation with uniform time stepping, this scheme leads to a numerical solution that suffers from the singularity near t = 0. In order to frustrate this singularity, a nonstandard higher-order L1-approximation for a nonuniform time-stepping scheme is developed. The developed scheme's convergence and unconditionally stability analysis have been verified. Numerical results effectively validate the theoretical aspects.Article Citation - WoS: 32Citation - Scopus: 30Analysis of the Fractional Corona Virus Pandemic Via Deterministic Modeling(Wiley, 2021) Tri, Vo Viet; Baleanu, Dumitru; Tuan, Nguyen HuyWith every passing day, one comes to know that cases of the corona virus disease are increasing. This is an alarming situation in many countries of the globe. So far, the virus has attacked as many as 188 countries of the world and 5 549 131 (27 May 2020) human population is affected with 348 224 deaths. In this regard, public and private health authorities are looking for manpower with modeling skills and possible vaccine. In this research paper, keeping in view the fast transmission dynamics of the virus, we have proposed a new mathematical model of eight mutually distinct compartments with the help of memory-possessing operator of Caputo type. The fractional order parameter psi of the model has been optimized so that smallest error can be attained while comparing simulations and the real data set which is considered for the country Pakistan. Using Banach fixed point analysis, it has been shown that the model has a unique solution whereas its basic reproduction numberR0is approximated to be 6.5894. Disease-free steady state is shown to be locally asymptotically stable forR0<0, otherwise unstable. Nelder-Mead optimization algorithm under MATLAB Toolbox with daily real cases of the virus in Pakistan is employed to obtain best fitted values of the parameters for the model's validation. Numerical simulations of the model have come into good agreement with the practical observations wherein social distancing, wearing masks, and staying home have proved to be the most effective measures in order to prevent the virus from further spread.
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