Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 8Citation - Scopus: 11Novel Diamond Alpha Bennett-Leindler Type Dynamic Inequalities and Their Applications(Springernature, 2022) Kayar, Zeynep; Kaymakcalan, BillurFor the exponent zeta > 1, the diamond alpha Bennett-Leindler type inequalities are established by developing two methods, one of which is based on the convex linear combinations of the related delta and nabla inequalities, while the other one is new and is implemented by using time scale calculus rather than algebra. These inequalities can be considered as the complementary to the classical ones obtained for 0 < zeta < 1. Since both methods provide different diamond alpha Bennett-Leindler type inequalities, we can obtain various diamond alpha unifications of the known delta and nabla BennettLeindler type inequalities. Moreover, the second method offers new Bennett-Leindler type inequalities even for the special cases such as delta and nabla ones. Moreover, an application of dynamic Bennett-Leindler type inequalities to the oscillation theory of the second-order half linear dynamic equation is developed and presented for the first time ever.Article On the Maximal Subspaces of Discrete Hamiltonian Systems(Springernature, 2024) Bairamov, Elgiz; Ugurlu, EkinIn this paper, we consider a discrete Hamiltonian system on nonnegative integers, and using Sylvester's inertia indices theory, we construct maximal subspaces on which the Hermitian form has a certain sign. After constructing nested ellipsoids, we introduce a lower bound for the number of linearly independent summable-square solutions of the discrete equation. Finally, we provide a limit-point criterion.Article Citation - WoS: 48Citation - Scopus: 50Hermite-Hadamard Type Inequalities for Interval-Valued Preinvex Functions Via Fractional Integral Operators(Springernature, 2022) Sahoo, Soubhagya Kumar; Mohammed, Pshtiwan Othman; Baleanu, Dumitru; Kodamasingh, Bibhakar; Srivastava, Hari MohanIn this article, the notion of interval-valued preinvex functions involving the Riemann-Liouville fractional integral is described. By applying this, some new refinements of the Hermite-Hadamard inequality for the fractional integral operator are presented. Some novel special cases of the presented results are discussed as well. Also, some examples are presented to validate our results. The established outcomes of our article may open another direction for different types of integral inequalities for fractional interval-valued functions, fuzzy interval-valued functions, and their associated optimization problems.Article Citation - WoS: 33Citation - Scopus: 33A General Fractional Pollution Model for Lakes(Springernature, 2022) Baleanu, Dumitru; Shiri, BabakA model for the amount of pollution in lakes connected with some rivers is introduced. In this model, it is supposed the density of pollution in a lake has memory. The model leads to a system of fractional differential equations. This system is transformed into a system of Volterra integral equations with memory kernels. The existence and regularity of the solutions are investigated. A high-order numerical method is introduced and analyzed and compared with an explicit method based on the regularity of the solution. Validation examples are supported, and some models are simulated and discussed.Article Citation - WoS: 6Citation - Scopus: 7Regular Fifth-Order Boundary Value Problems(Springernature, 2020) Ugurlu, EkinThe main purpose of this paper is to introduce a method to handle some boundary value problems generated by fifth-order formally symmetric differential equation and separated, real-coupled and complex-coupled boundary conditions. Moreover, the continuity properties of the eigenvalues of these problems on some data are studied and some Frechet derivatives of the eigenvalues are introduced.Article Citation - WoS: 16Citation - Scopus: 21Using Anns Approach for Solving Fractional Order Volterra Integro-Differential Equations(Springernature, 2017) Rostami, Fariba; Golmankhaneh, Alireza K.; Baleanu, Dumitru; Jafarian, AhmadIndeed, interesting properties of artificial neural networks approach made this non-parametric model a powerful tool in solving various complicated mathematical problems. The current research attempts to produce an approximate polynomial solution for special type of fractional order Volterra integrodifferential equations. The present technique combines the neural networks approach with the power series method to introduce an efficient iterative technique. To do this, a multi-layer feed-forward neural architecture is depicted for constructing a power series of arbitrary degree. Combining the initial conditions with the resulted series gives us a suitable trial solution. Substituting this solution instead of the unknown function and employing the least mean square rule, converts the origin problem to an approximated unconstrained optimization problem. Subsequently, the resulting nonlinear minimization problem is solved iteratively using the neural networks approach. For this aim, a suitable three-layer feed-forward neural architecture is formed and trained using a back-propagation supervised learning algorithm which is based on the gradient descent rule. In other words, discretizing the differential domain with a classical rule produces some training rules. By importing these to designed architecture as input signals, the indicated learning algorithm can minimize the defined criterion function to achieve the solution series coefficients. Ultimately, the analysis is accompanied by two numerical examples to illustrate the ability of the method. Also, some comparisons are made between the present iterative approach and another traditional technique. The obtained results reveal that our method is very effective, and in these examples leads to the better approximations.