Browsing by Author "Akgul, Esra Karatas"

Now showing 1 - 9 of 9

Citation - WoS: 1
Citation - Scopus: 2
A Homotopy Perturbation Solution for Solving Highly Nonlinear Fluid Flow Problem Arising in Mechanical Engineering
(Amer inst Physics, 2018) Khan, Yasir; Baleanu, Dumitru; Akgul, Ali; Faraz, Naeem; Inc, Mustafa; Akgul, Esra Karatas; Baleanu, Dumitru; 56389; Matematik
In this paper, a highly nonlinear equations are treated analytically via homotopy perturbation method for fluid mechanics problem. The non-linear differential equations are transformed to a coupled non-linear ordinary, differential equations via similarity transformations. Graphical results are presented and discussed for various physical parameters.
Citation - WoS: 29
Citation - Scopus: 32
A novel method for analysing the fractal fractional integrator circuit
(Elsevier, 2021) Akgul, Ali; Baleanu, Dumitru; Ahmad, Shabir; Ullah, Aman; Baleanu, Dumitru; Akgul, Esra Karatas; 56389; Matematik
In this article, we propose the integrator circuit model by the fractal-fractional operator in which fractional-order has taken in the Atangana-Baleanu sense. Through Schauder's fixed point theorem, we establish existence theory to ensure that the model posses at least one solution and via Banach fixed theorem, we guarantee that the proposed model has a unique solution. We derive the results for Ulam-Hyres stability by mean of non-linear functional analysis which shows that the proposed model is Ulam-Hyres stable under the new fractal-fractional derivative. We establish the numerical results of the model under consideration through Atanaga-Toufik method. We simulate the numerical results for different sets of fractional order and fractal dimension.(C) 2021 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/).
Citation - WoS: 1
Comparison on Solving a Class of Nonlinear Systems of Partial Differential Equations and Multiple Solutions of Second Order Differential Equations
(Springer international Publishing Ag, 2019) Akgul, Ali; Baleanu, Dumitru; Akgul, Esra Karatas; Khan, Yasir; Baleanu, Dumitru; 56389; Matematik
Citation - WoS: 31
Citation - Scopus: 38
Laplace transform method for economic models with constant proportional caputo derivative
(Mdpi, 2020) Akgul, Esra Karatas; Baleanu, Dumitru; Akgul, Ali; Baleanu, Dumitru; 56389; Matematik
In this study, we solved the economic models based on market equilibrium with constant proportional Caputo derivative using the Laplace transform. We proved the accuracy and efficiency of the method. We constructed the relations between the solutions of the problems and bivariate Mittag-Leffler functions.
Citation - WoS: 4
Citation - Scopus: 6
New Numerical Method for Solving Tenth Order Boundary Value Problems
(Mdpi, 2018) Akgul, Ali; Baleanu, Dumitru; Akgul, Esra Karatas; Baleanu, Dumitru; Inc, Mustafa; 56389; Matematik
In this paper, we implement reproducing kernel Hilbert space method to tenth order boundary value problems. These problems are important for mathematicians. Different techniques were applied to get approximate solutions of such problems. We obtain some useful reproducing kernel functions to get approximate solutions. We obtain very efficient results by this method. We show our numerical results by tables.
Citation - WoS: 7
Citation - Scopus: 8
Representation for the reproducing kernel Hilbert space method for a nonlinear system
(Hacettepe Univ, Fac Sci, 2019) Akgul, Esra Karatas; Baleanu, Dumitru; Akgul, Ali; Khan, Yasir; Baleanu, Dumitru; 56389; Matematik
We apply the reproducing kernel Hilbert space method to a nonlinear system in this work. We utilize this technique to overcome the nonlinearity of the problem. We obtain accurate results. We demonstrate our results by tables and figures. We prove the efficiency of the method.
Citation - WoS: 0
Citation - Scopus: 0
Reproducing Kernel Method for Strongly Non-linear Equation
(Amer inst Physics, 2018) Akgul, Ali; Baleanu, Dumitru; Akgul, Esra Karatas; Baleanu, Dumitru; 56389; Matematik
In this paper, we search the efficiency of the reproducing kernel method (RKM) in solving the strongly nonlinear equation. An example is presented to prove the power of the technique. The results attained from the technique are compared with the other techniques. Results prove that the presented technique is very effective.
Citation - WoS: 23
Solutions of nonlinear systems by reproducing kernel method
(int Scientific Research Publications, 2017) Akgul, Ali; Baleanu, Dumitru; Khan, Yasir; Akgul, Esra Karatas; Baleanu, Dumitru; Al Qurashi, Maysaa Mohamed; 56389; Matematik
A novel approximate solution is obtained for viscoelastic fluid model by reproducing kernel method (RKM). The resulting equation for viscoelastic fluid with magneto-hydrodynamic flow is transformed to the nonlinear system by introducing the dimensionless variables. Results are presented graphically to study the efficiency and accuracy of the reproducing kernel method. Results show that this method namely RKM is an efficient method for solving nonlinear system in any engineering field. (C) 2017 All rights reserved.
Citation - WoS: 2
Solving the Nonlinear System of Third-Order Boundary Value Problems
(Springer international Publishing Ag, 2019) Akgul, Ali; Baleanu, Dumitru; Akgul, Esra Karatas; Khan, Yasir; Baleanu, Dumitru; 56389; Matematik