Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
Browse
8 results
Search Results
Article Citation - WoS: 34Citation - Scopus: 36Exact Solutions of Boussinesq and Kdv-Mkdv Equations by Fractional Sub-Equation Method(Editura Acad Romane, 2013) Jafari, Hossein; Baleanu, Dumitru; Tajadodi, Haleh; Baleanu, Dumitru; Al-Zahrani, Abdulrahim A.; Alhamed, Yahia A.; Zahid, Adnan H.; MatematikA fractional sub-equation method is introduced to solve fractional differential equations. By the aid of the solutions of the fractional Riccati equation, we construct solutions of the Boussinesq and KdV-mKdV equations of fractional order. The obtained results show that this method is very efficient and easy to apply for solving fractional partial differential equations.Article Citation - WoS: 31Citation - Scopus: 40New Solutions of the Fractional Differential Equations With Modified Mittag-Leffler Kernel(Asme, 2023) Baleanu, Dumitru; Odibat, ZaidThis paper is concerned with some features of the modified Caputo-type Mittag-Leffler fractional derivative operator and its associated fractional integral operator. Mainly, new types of solutions for fractional differential equations with Mittag-Leffler kernel are generated based on a numerical algorithm developed in this paper. The suggested algorithm is used to describe the solution behavior of models involving modified Caputo-type Mittag-Leffler fractional derivatives. The results described in this paper are expected to be effectively employed in the area of simulating related fractional models.Article Citation - WoS: 9Citation - Scopus: 11Research on a Collocation Approach and Three Metaheuristic Techniques Based on Mvo, Mfo, and Woa for Optimal Control of Fractional Differential Equation(Sage Publications Ltd, 2023) Khanduzi, Raheleh; Beik, Samaneh P. A.; Baleanu, Dumitru; Ebrahimzadeh, Asiyeh; A Beik, Samaneh PExploiting a comprehensive mathematical model for a class of systems governed by fractional optimal control problems is the significant focal point of the current paper. The efficiency index is a function of both control and state variables and the dynamic control system relies on Caputo fractional derivatives. The attributes of Bernoulli polynomials and their operational matrices of fractional Riemann-Liouville integrations are applied to convert the optimization problem to the nonlinear programing problem. Executing multi-verse optimizer, moth-flame optimization, and whale optimization algorithm terminate to the most excellent solution of fractional optimal control problems. A study on the advantage and performance between these approaches is analyzed by some examples. Comprehensive analysis ascertains that moth-flame optimization significantly solves the example. Furthermore, the privilege and advantage of preference with its accuracy are numerically indicated. Finally, results demonstrate that the objective function value gained by moth-flame optimization in comparison with other algorithms effectively decreased.Article Citation - WoS: 61Citation - Scopus: 83Impulsive Caputo-Fabrizio Fractional Differential Equations in B-Metric Spaces(de Gruyter Poland Sp Z O O, 2021) Abbas, Said; Benchohra, Mouffak; Karapinar, Erdal; Lazreg, Jamal Eddine; Karaplnar, ErdalWe deal with some impulsive Caputo-Fabrizio fractional differential equations in b-metric spaces. We make use of alpha-phi-Geraghty-type contraction. An illustrative example is the subject of the last section.Article Citation - WoS: 12Citation - Scopus: 10Fractional-Order Investigation of Diffusion Equations Via Analytical Approach(Frontiers Media Sa, 2021) Khan, Hassan; Mustafa, Saima; Mou, Lianming; Baleanu, Dumitru; Liu, HaobinThis research article is mainly concerned with the analytical solution of diffusion equations within a Caputo fractional-order derivative. The motivation and novelty behind the present work are the application of a sophisticated and straight forward procedure to solve diffusion equations containing a derivative of a fractional-order. The solutions of some illustrative examples are calculated to confirm the closed contact between the actual and the approximate solutions of the targeted problems. Through analysis it is shown that the proposed solution has a higher rate of convergence and provides a closed-form solution. The small number of calculations is the main advantage of the proposed method. Due to a comfortable and straight forward implementation, the suggested method can be utilized to nonlinear fractional-order problems in various applied science branches. It can be extended to solve other physical problems of fractional-order in multiple areas of applied sciences.Article Citation - WoS: 1Citation - Scopus: 1Fractional Differential Equation With a Complex Potential(Univ Nis, Fac Sci Math, 2020) Ugurlu, Ekin; Tas, Kenan; Baleanu, DumitruIn this manuscript, we discuss the square-integrable property of a fractional differential equation having a complex-valued potential function and we show that at least one of the linearly independent solutions of the fractional differential equation must be squarely integrable with respect to some function containing the imaginary parts of the spectral parameter and the potential function.Article Citation - WoS: 64Citation - Scopus: 78Artificial Neural Network Approach for a Class of Fractional Ordinary Differential Equation(Springer London Ltd, 2017) Mokhtarpour, Masoumeh; Baleanu, Dumitru; Jafarian, AhmadThe essential characteristic of artificial neural networks which against the logistic traditional systems is a data-based approach and has led a number of higher education scholars to investigate its efficacy, during the past few decades. The aim of this paper was concerned with the application of neural networks to approximate series solutions of a class of initial value ordinary differential equations of fractional orders, over a bounded domain. The proposed technique uses a suitable truncated power series of the solution function and transforms the original differential equation in a minimization problem. Then, the minimization problem is solved using an accurate neural network model to compute the parameters with high accuracy. Numerical results are given to validate the iterative method.Article Citation - WoS: 10Citation - Scopus: 9On the Existence Interval for the Initial Value Problem of a Fractional Differential Equation(Hacettepe Univ, Fac Sci, 2011) Mustafa, Octavian G.; Baleanu, DumitruWe compute via a comparison function technique, a new bound for the existence interval of the initial value problem for a fractional differential equation given by means of Caputo derivatives. We improve in this way the estimate of the existence interval obtained very recently in the literature.