Browsing by Author "Aslan, Ersin"

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Citation - WoS: 12
Citation - Scopus: 10
An Advanced Method With Convergence Analysis for Solving Space-Time Fractional Partial Differential Equations With Multi Delays
(Springer Heidelberg, 2019) Kürkçü, ÖmÜr Kıvanç; Aslan, Ersin; Sezer, Mehmet
This study considers the space-time fractional partial differential equations with multi delays under a unique formulation, proposing a numerical method involving advanced matrix system. This matrix system is made up of the matching polynomial of complete graph together with fractional Caputo and Jumarie derivative types. Also, the derivative types are scrutinized to determine which of them is more proper for the method. Convergence analysis of the method is established via an average value of residual function using double integrals. The obtained solutions are improved with the aid of a residual error estimation. A general computer program module, which contains few steps, is developed. Tables and figures prove the efficiency and simplicity of the method. Eventually, an algorithm is given to illustrate the basis of the method.
Citation - WoS: 8
Citation - Scopus: 8
An Integrated Numerical Method With Error Analysis for Solving Fractional Differential Equations of Quintic Nonlinear Type Arising in Applied Sciences
(Wiley, 2019) Kürkçü, ÖmÜr Kıvanç; Aslan, Ersin; Sezer, Mehmet
In this study, fractional differential equations having quintic nonlinearity are considered by proposing an accurate numerical method based on the matching polynomial and matrix-collocation system. This method provides an integration between matrix and fractional derivative, which makes it fast and efficient. A hybrid computer program is designed by making use of the fast algorithmic structure of the method. An error analysis technique consisting of the fractional-based residual function is constructed to scrutinize the precision of the method. Some error tests are also performed. Figures and tables present the consistency of the approximate solutions of highly stiff model problems. All results point out that the method is effective, simple, and eligible.
Citation - WoS: 10
Citation - Scopus: 11
An Inventive Numerical Method for Solving the Most General Form of Integro-Differential Equations With Functional Delays and Characteristic Behavior of Orthoexponential Residual Function
(Springer Heidelberg, 2019) Kürkçü, Ömür Kıvanç; Aslan, Ersin; Sezer, Mehmet
In this study, we constitute the most general form of functional integro-differential equations with functional delays. An inventive method based on Dickson polynomials with the parameter- along with collocation points is employed to solve them. The stability of the solutions is simulated according to an interval of the parameter-. A useful computer program is developed to obtain the precise values from the method. The residual error analysis is used to improve the obtained solutions. The characteristic behavior of the residual function is established with the aid of the orthoexponential polynomials. We compare the present numerical results of the method with those obtained by the existing methods in tables.
Citation - WoS: 11
Citation - Scopus: 11
A Novel Graph-Operational Matrix Method for Solving Multidelay Fractional Differential Equations With Variable Coefficients and a Numerical Comparative Survey of Fractional Derivative Types
(Scientific Technical Research Council Turkey-Tubitak, 2019) Kürkçü, ÖmÜr Kıvanç; Aslan, Ersin; Sezer, Mehmet
In this study, we introduce multidelay fractional differential equations with variable coefficients in a unique formula. A novel graph-operational matrix method based on the fractional Caputo, Riemann-Liouville, Caputo-Fabrizio, and Jumarie derivative types is developed to efficiently solve them. We also make use of the collocation points and matrix relations of the matching polynomial of the complete graph in the method. We determine which of the fractional derivative types is more appropriate for the method. The solutions of model problems are improved via a new residual error analysis technique. We design a general computer program module. Thus, we can explicitly monitor the usefulness of the method. All results are scrutinized in tables and figures. Finally, an illustrative algorithm is presented.
Citation - WoS: 4
Citation - Scopus: 3
A Novel Hybrid Method for Solving Combined Functional Neutral Differential Equations With Several Delays and Investigation of Convergence Rate Via Residual Function
(Univ Tabriz, 2019) Kürkçü, ÖmÜr Kıvanç; Aslan, Ersin; Sezer, Mehmet
In this study, we introduce a novel hybrid method based on a simple graph along with operational matrix to solve the combined functional neutral differential equations with several delays. The matrix relations of the matching polynomials of complete and path graphs are employed in the matrix-collocation method. We improve the obtained solutions via an error analysis technique. The oscillation of them on time interval is also estimated by coupling the method with Laplace-Pade technique. We develop a general computer program and so we can efficiently monitor the precision of the method. We investigate a convergence rate of the method by constructing a formula based on the residual function. Eventually, an algorithm is described to show the easiness of the method.
Citation - WoS: 18
Citation - Scopus: 17
A Numerical Approach Technique for Solving Generalized Delay Integro-Differential Equations With Functional Bounds by Means of Dickson Polynomials
(World Scientific Publ Co Pte Ltd, 2018) Kürkçü, ÖmÜr Kıvanç; Aslan, Ersin; Sezer, Mehmet; Ilhan, Ozgul
In this study, we have considered the linear classes of differential-(difference), integro-differential-(difference) and integral equations by constituting a generalized form, which contains proportional delay, difference, differentiable difference or delay. To solve the generalized form numerically, we use the efficient matrix technique based on Dickson polynomials with the parameter-a along with the collocation points. We also encode the useful computer program for susceptibility of the technique. The residual error analysis is implemented by using the residual function. The consistency of the technique is analyzed. Also, the numerical results illustrated in tables and figures are compared.