Browsing by Author "Kurt, A."

Now showing 1 - 3 of 3

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; 06.04. Endüstri Mühendisliği; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 06. Mühendislik Fakültesi; 01. Çankaya Üniversitesi; 09. Rektörlük; 09.02. Yabancı Diller Bölümü
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: 43
Citation - Scopus: 50
New Solutions for Conformable Fractional Nizhnik-Novikov System Via G'/g Expansion Method and Homotopy Analysis Methods
(Springer, 2017) Tasbozan, O.; Baleanu, D.; Kurt, A.; 02.02. Matematik; 06.04. Endüstri Mühendisliği; 02. Fen-Edebiyat Fakültesi; 06. Mühendislik Fakültesi; 01. Çankaya Üniversitesi; 09. Rektörlük; 09.02. Yabancı Diller Bölümü
The main purpose of this paper is to find the exact and approximate analytical solution of Nizhnik-Novikov-Veselov system which may be considered as a model for an incompressible fluid with newly defined conformable derivative by using G'/G expansion method and homotopy analysis method (HAM) respectively. Authors used conformable derivative because of its applicability and lucidity. It is known that, the NNV system of equations is an isotropic Lax integrable extension of the well-known KdV equation and has physical significance. Also, NNV system of equations can be derived from the inner parameter-dependent symmetry constraint of the KP equation. Then the exact solutions obtained by using G'/G expansion method are compared with the approximate analytical solutions attained by employing HAM.
Citation - WoS: 4
Citation - Scopus: 4
Unrelated Parallel Machine Scheduling Under Machine Availability and Eligibility Constraints To Minimize the Makespan of Non-Resumable Jobs
(Univ Novi Sad, Fac Technical Sciences, 2024) Kurt, A.; Cetinkaya, F. C.; 06.04. Endüstri Mühendisliği; 06. Mühendislik Fakültesi; 01. Çankaya Üniversitesi; 09. Rektörlük; 09.02. Yabancı Diller Bölümü
This study considers the scheduling problem of multiple independent and non-resumable jobs on unrelated parallel machines subject to machine availability and eligibility constraints. For each machine, there is a maximum continuous working time due to an unavailable period required for maintenance or tool changeover so that multiple unavailable periods on each machine may occur. The start time of an unavailable period on each machine is flexible and depends on the sum of the processing times of all jobs completed before this unavailability period. The objective is to minimize the makespan, which is the time to complete the processing of all non-resumable jobs. We develop a mixed integer linear programming (MILP) model to solve the problem optimally and a heuristic algorithm to solve the problem instances for which the MILP model cannot achieve an optimal solution in a reasonable allowed solution time. Computational experiments are done to evaluate our solution approaches' performance in terms of quality and time. The results show that using a mixed integer linear programming model is not a practical alternative, especially for large -sized problem instances. However, the proposed heuristic algorithm finds near -optimal solutions in a very short time.