Matematik Bölümü Yayın Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413

Browse

Now showing 1 - 20 of 115

Citation - WoS: 64
Citation - Scopus: 63
An Accurate Numerical Technique for Solving Fractional Optimal Control Problems
(Editura Acad Romane, 2015) Bhrawy, A. H.; Baleanu, Dumitru; Doha, E. H.; Baleanu, D.; Ezz-Eldien, S. S.; Abdelkawy, M. A.; 56389; Matematik
In this article, we propose the shifted Legendre orthonormal polynomials for the numerical solution of the fractional optimal control problems that appear in several branches of physics and engineering. The Rayleigh-Ritz method for the necessary conditions of optimization and the operational matrix of fractional derivatives are used together with the help of the properties of the shifted Legendre orthonormal polynomials to reduce the fractional optimal control problem to solving a system of algebraic equations that greatly simplifies the problem. For confirming the efficiency and accuracy of the proposed technique, an illustrative numerical example is introduced with its approximate solution.
Citation - Scopus: 1
Adapting Integral Transforms To Create Solitary Solutions for Partial Differential Equations Via a New Approach
(New York Business Global Llc, 2023) Baleanu, Dumitru; Saadeh, Rania; Qazza, Ahmad; Burqan, Aliaa; 56389
In this article, a new effective technique is implemented to solve families of nonlinear partial differential equations (NLPDEs). The proposed method combines the double ARA-Sumudu transform with the numerical iterative method to get the exact solutions of NLPDEs. The suc-cessive iterative method was used to find the solution of nonlinear terms of these equations. In order to show the efficiency and applicability of the presented method, some physical applications are analyzed and illustrated, and to defend our results, some numerical examples and figures are discussed.
Citation - Scopus: 1
Advanced Mathematical and Statistical Tools in the Dynamic Modeling and Simulation of Gene-Environment Regulatory Networks
(Springer New York LLC, 2014) Purutçuoğlu, V.; Weber, G.-W.; Defterli, Ö.; 31401
Citation - Scopus: 6
Advanced Topics in Fractional Differential Equations a Fixed Point Approach
(Springer Nature, 2023) Benchohra, M.; Karapınar, Erdal; Karapınar, E.; Lazreg, J.E.; Salim, A.; 19184; Matematik
Citation - Scopus: 3
Algorithmic Complexity-Based Fractional-Order Derivatives in Computational Biology
(Springer Science and Business Media Deutschland GmbH, 2023) Baleanu, D.; Karaca, Y.; 56389
Fractional calculus approach, providing novel models through the introduction of fractional-order calculus to optimization methods, is employed in machine learning algorithms. This scheme aims to attain optimized solutions by maximizing the accuracy of the model and minimizing the functions like the computational burden. Mathematical-informed frameworks are to be employed to enable reliable, accurate, and robust understanding of various complex biological processes that involve a variety of spatial and temporal scales. This complexity requires a holistic understanding of different biological processes through multi-stage integrative models that are capable of capturing the significant attributes on the related scales. Fractional-order differential and integral equations can provide the generalization of traditional integral and differential equations through the extension of the conceptions with respect to biological processes. In addition, algorithmic complexity (computational complexity), as a way of comparing the efficiency of an algorithm, can enable a better grasping and designing of efficient algorithms in computational biology as well as other related areas of science. It also enables the classification of the computational problems based on their algorithmic complexity, as defined according to the way the resources are required for the solution of the problem, including the execution time and scale with the problem size. Based on a novel mathematical informed framework and multi-staged integrative method concerning algorithmic complexity, this study aims at establishing a robust and accurate model reliant on the combination of fractional-order derivative and Artificial Neural Network (ANN) for the diagnostic and differentiability predictive purposes for the disease, (diabetes, as a metabolic disorder, in our case) which may display various and transient biological properties. Another aim of this study is benefitting from the concept of algorithmic complexity to obtain the fractional-order derivative with the least complexity in order that it would be possible to achieve the optimized solution. To this end, the following steps were applied and integrated. Firstly, the Caputo fractional-order derivative with three-parametric Mittag-Leffler function (α,β,γ) was applied to the diabetes dataset. Thus, new fractional models with varying degrees were established by ensuring data fitting through the fitting algorithm Mittag-Leffler function with three parameters (α,β,γ) based on heavy-tailed distributions. Following this application, the new dataset, named the mfc_diabetes, was obtained. Secondly, classical derivative (calculus) was applied to the diabetes dataset, which yielded the cd_diabetes dataset. Subsequently, the performance of the new dataset as obtained from the first step and of the dataset obtained from the second step as well as of the diabetes dataset was compared through the application of the feed forward back propagation (FFBP) algorithm, which is one of the ANN algorithms. Next, the fractional order derivative model which would be the most optimal for the disease was generated. Finally, algorithmic complexity was employed to attain the Caputo fractional-order derivative with the least complexity, or to achieve the optimized solution. This approach through the application of fractional-order calculus to optimization methods and the experimental results have revealed the advantage of maximizing the model’s accuracy and minimizing the cost functions like the computational costs, which points to the applicability of the method proposed in different domains characterized by complex, dynamic and transient components. © 2023, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
Citation - WoS: 7
Analysis O a Caputo Hiv and Malaria Co-Infection Epidemic Model
(Chiang Mai Univ, Fac Science, 2021) Ahmed, Idris; Jarad, Fahd; Yusuf, Abdullahi; Sani, Musbahu Aminu; Jarad, Fahd; Kumam, Wiyada; Thounthong, Phatiphat; 234808; Matematik
In this paper, we investigate a fractional-order compartmental HIV and Malaria co-infection epidemic model using the Caputo derivative. The existence and uniqueness of the solution to the proposed fractional-order model were investigated using fixed point theorem techniques. To demonstrate that the proposed fractional-order model is both mathematically and epidemiologically well-posed, we compute the model's positivity and boundedness, which is an important feature in epidemiology. Finally, we analyze the dynamic behavior of each of the state variables using a recent and powerful computational technique known as the fractional Euler method.
Analysis of Fractional Fokker-Planck Equation With Caputo and Caputo-Fabrizio Derivatives
(Univ Craiova, 2021) Cetinkaya, Suleyman; Baleanu, Dumitru; Demir, Ali; Baleanu, Dumitru; 56389; Matematik
This research focus on the determination of the numerical solution for the mathematical model of Fokker-Planck equations utilizing a new method, in which Sumudu transformation and homotopy analysis method (SHAM) are used together. By SHAM analytical series solution of any mathematical model including fractional derivative can be obtained. By this method, we constructed the solution of fractional Fokker-Planck equations in Caputo and Caputo-Fabrizio senses. The results show that this method is advantageous and applicable to form the series resolution of the fractional mathematical models.
Citation - WoS: 9
Analytic Study of Allen-Cahn Equation of Fractional Order
(int Center Scientific Research & Studies, 2017) Kumar, Devendra; Baleanu, Dumitru; Singh, Jagdev; Baleanu, Dumitru; 56389; Matematik
The key purpose of the present article is to analyze the Allen Cahn equation of fractional order. The fractional Allen-Cahn equation models the process of phase separation in iron alloys, along with order-disorder transitions. The analytical technique is employed to investigate the fractional model of Allen-Cahn equation. The numerical results are shown graphically. The outcomes show that the analytical technique is very efficient and user friendly for handling nonlinear fractional differential equations describing the real world problems.
Citation - Scopus: 1
Analytical and Numerical Solutions for Time-Fractional New Coupled Mkdv Equation Arising in Interaction of Two Long Waves
(Asia Pacific Academic, 2019) Şenol, M.; Kurt, A.; Baleanu, D.; Tasbozan, O.; 56389
The aim of this paper is to present new exact solution sets of nonlinear conformable time-fractional new coupled mKdV equations which arise in interaction of two long waves with different dispersion relations by means of sub-equation method. In addition, we also propose an analytical-approximate method namely residual power series method (RPSM) for the system. The fractional derivatives have been explained in newly defined conformable type, during the solution procedure. The exact solutions of the system obtained by the sub-equation method have been compared to approximate solutions derived by RPSM. The results showed that both methods are robust, dependable, easy to apply and a good alternative for seeking solutions of fractional partial differential equations. © 2019 Asia Pacific Journal of Mathematics.
Citation - WoS: 5
Citation - Scopus: 6
Application of Sumudu and Double Sumudu Transforms To Caputo-Fractional Differential Equations
(Eudoxus Press, Llc, 2012) Jarad, Fahd; Jarad, Fahd; Tas, K.; Taş, Kenan; 4971; Matematik
The definition, properties and applications of the Sumudu transform to ordinary differential equations are described in [1-3]. In this manuscript we derive the formulae for the Sumudu and double Sumudu transforms of ordinary and partial fractional derivatives and apply them in solving Caputo-fractional differential equations. Our purpose here is to show the applicability of this new transform and its efficiency in solving such problems.
Citation - Scopus: 20
Applications of Short Memory Fractional Differential Equations With Impulses
(L and H Scientific Publishing, LLC, 2023) Wu, G.-C.; Baleanu, D.; Shiri, B.; 56389
Dynamical systems’ behavior is sometimes varied with some impulse and sudden changes in process. The dynamics of these systems can not be modeled by previous concepts of derivative or fractional derivatives any longer. The short memory concept is a solution and a better choice for fractional modeling of such processes. We apply short memory fractional differential equations for these systems. We propose collocation methods based on piecewise polynomials to approximate solutions of these equations. We provide various examples to demonstrate the application of the short memory derivative for impulse systems and efficiency of the presented numerical methods. © 2023 L&H Scientific Publishing, LLC. All rights reserved
Approximate Controllability Results for Impulsive Partial Functional Nonlocal Integro-Differential Evolution Systems Through Resolvent Operators
(L and H Scientific Publishing, LLC, 2018) Suganya, S.; Baleanu, D.; Arjunan, M.M.; Nagaraj, M.; 56389
This paper investigates the existence and approximate controllability results for a class of impulsive functional integro-differential evolution systems with nonlocal conditions via resolvent operators in Banach spaces. By making utilization of Banach contraction principle and Schaefer's fixed point theorem along with resolvent operators and semigroup theory, we build up the desired results. As an application, we also consider an impulsive partial functional integro-differential equations. © 2018 L & H Scientific Publishing, LLC.
Citation - WoS: 105
Citation - Scopus: 111
Approximate Solutions for Diffusion Equations on Cantor Space-Time
(Editura Acad Romane, 2013) Yang, Xiao-Jun; Baleanu, Dumitru; Baleanu, Dumitru; Zhong, Wei-Ping; 56389; Matematik
In this paper we investigate diffusion equations on Cantor space-time and we obtain approximate solutions by using the local fractional Adomian decomposition method derived from the local fractional operators. Analytical solutions are given in terms of the Mittag-Leffler functions defined on Cantor sets.
Citation - WoS: 17
Citation - Scopus: 13
Best Proximity Points for Cyclical Contraction Mappings With 0-Boundedly Compact Decompositions
(Eudoxus Press, Llc, 2013) Abdeljawad, Thabet; Abdeljawad, T.; Alzabut, J. O.; Alzabut, Jehad; Mukheimer, A.; Zaidan, Y.; Matematik
The existence of best proximity points for cyclical type contraction mappings is proved in the category of partial metric spaces. The concept of 0-boundedly compact is introduced and used in the cyclical decomposition. Some possible generalizations to the main results are discussed. Further, illustrative examples are given to demonstrate the effectiveness of our results.
Citation - WoS: 11
Citation - Scopus: 11
Best Proximity Results on Condensing Operators Via Measure of Noncompactness With Application To Integral Equations
(Chiang Mai Univ, Fac Science, 2020) Gabeleh, Moosa; Karapınar, Erdal; Asadi, Mehdi; Karapinar, Erdal; 19184; Matematik
We prove the best proximity point results for condensing operators on C-class of functions, by using a concept of measure of noncompactness. The results are applied to show the existence of a solution for certain integral equations. We express also an illsutrative examples to indicate the validity of the observed results.
Citation - WoS: 6
Citation - Scopus: 6
A Caputo Fractional Order Boundary Value Problem With Integral Boundary Conditions
(Eudoxus Press, Llc, 2013) Babakhani, Azizollah; Abdeljawad, Thabet; Abdeljawad, Thabet; Matematik
In this paper, we discuss existence and uniqueness of solutions to nonlinear fractional order ordinary differential equations with integral boundary conditions in an ordered Banach space. We use the Caputo fractional differential operator and the nonlinearity depends on the fractional derivative of an unknown function. The nonlinear alternative of the Leray- Schauder type Theorem is the main tool used here to establish the existence and the Banach contraction principle to show the uniqueness of the solution under certain conditions. The compactness of solutions set is also investigated and an example is included to show the applicability of our results.
Citation - Scopus: 5
Chaos Synchronization of the Fractional Rucklidge System Based on New Adomian Polynomials
(L and H Scientific Publishing, LLC, 2017) Baleanu, D.; Huang, L.-L.; Wu, G.-C.; 56389
The fractional Rucklidge system is a new kind of chaotic models which hold the feature of memory effects and can depict the long history interactions. A numerical formula is proposed by use of the fast Adomian polynomials. Chaotic behavior are discussed and the Poincare sections are given for various fractional cases. It's also applied in chaos synchronization of the fractional system. © 2017 L & H Scientific Publishing, LLC.
Citation - WoS: 25
A Chebyshev-Laguerre Collocation Scheme for Solving A Time Fractional Sub-Diffusion Equation on A Semi-Infinite Domain
(Editura Acad Romane, 2015) Bhrawy, A. H.; Baleanu, Dumitru; Abdelkawy, M. A.; Alzahrani, A. A.; Baleanu, D.; Alzahrani, E. O.; Matematik
We propose a new efficient spectral collocation method for solving a time fractional sub-diffusion equation on a semi-infinite domain. The shifted Chebyshev-Gauss-Radau interpolation method is adapted for time discretization along with the Laguerre-Gauss-Radau collocation scheme that is used for space discretization on a semi-infinite domain. The main advantage of the proposed approach is that a spectral method is implemented for both time and space discretizations, which allows us to present a new efficient algorithm for solving time fractional sub-diffusion equations.
Chemometric Calibration Based on the Wavelet Transform for the Quantitative Resolution of Two-Colorant Mixtures
(Editura Acad Romane, 2005) Baleanu, Dumitru; Dinç, E; Baleanu, D; Taş, Kenan; Üstundag, O; Tas, K; 56389; 4971; Matematik
In this study we proposed a wavelet transform (WT) followed by two chemometric techniques for the quantitative determination of sunset yellow (SUN) and tartrazine (TAR) in their market samples. Absorbances of the concentration set formed by TAR and SUN mixtures were measured between 335-575 nm at 480 points with 0.5 nm intervals and their absorbance values as absorbance data vectors were transferred into the wavelets domain. A continuous wavelet transform (CWT) was applied, to the absorbance data. The obtained CWT-coefficients (x-block) and concentration set (y-block) were used for the construction of the principal component regression (VCR) and partial least squares (PLS) calibrations. Good results were reported for the application of the combining wavelets and chemometric tools in the determination of colorants in samples.
Citation - WoS: 5
Citation - Scopus: 6
Coincidence Point Theorem on Hilbert Spaces Via Weak Ekeland Variational Principle and Application To Boundary Value Problem
(Chiang Mai Univ, Fac Science, 2021) Asadi, Mehdi; Karapınar, Erdal; Karapinar, Erdal; 19184; Matematik
In this paper, we give a new coincidence point theorem for two operators on Hilbert spaces for certain operators by using the weak Ekeland variational principle. Our paper extends and improves the results on the topic in the literature. We consider a boundary value problem as an application of our results.

Browse

Browsing Matematik Bölümü Yayın Koleksiyonu by Scopus Q "Q4"