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BibTex RIS Kaynak Göster

Yıl 2020, Cilt: 8 Sayı: 2, 337 - 342, 27.10.2020

Süleyman Çetinkaya Ali Demir

Öz

Kaynakça

  • [1] A. Demir, M. A. Bayrak and E. Ozbilge, New approaches for the solution of space-time fractional Schr¨odinger equation, Advances in Difference Equation, Vol. 2020:133, (2020).
  • [2] A. Demir and M. A. Bayrak, A New Approach for the Solution of Space-TimeFractional Order Heat-Like Partial Differential Equations by Residual Power Series Method, Communications in Mathematics and Applications, Vol. 10, No. 3 (2019), 585–597.
  • [3] A. Demir, M. A. Bayrak and E. Ozbilge, A New Approach for the Approximate AnalyticalSolution of Space-Time Fractional Differential Equations by the Homotopy Analysis Method, Advances in Mathematical Physics, Vol. 2019, Article ID 5602565, (2019).
  • [4] A. Demir, M. A. Bayrak and E. Ozbilge, An Approximate Solution of the Time-Fractional FisherEquation with Small Delay by Residual Power Series Method, Mathematical Problems in Engineering, Vol. 2018, Article ID 9471910, (2018).
  • [5] S. Cetinkaya, A. Demir and H. Kodal Sevindir, The analytic solution of initial boundary value problem including time-fractional diffusion equation, Facta Universitatis Ser. Math. Inform, Vol. 35, No. 1 (2020), 243-252.
  • [6] S. Cetinkaya, A. Demir, and H. Kodal Sevindir, The analytic solution of sequential space-time fractional diffusion equation including periodic boundary conditions, Journal of Mathematical Analysis, Vol. 11, No.1 (2020), 17-26.
  • [7] S. Cetinkaya and A. Demir, The Analytic Solution of Time-Space Fractional Diffusion Equation via New Inner Product with Weighted Function, Communications in Mathematics and Applications, Vol. 10, No. 4 (2019), 865-873.
  • [8] S. Cetinkaya, A. Demir, and H. Kodal Sevindir, The Analytic Solution of Initial Periodic Boundary Value Problem Including Sequential Time Fractional Diffusion Equation, Communications in Mathematics and Applications, Vol. 11, No. 1 (2020), 173-179.
  • [9] A. A. Kilbas, H. M. Srivastava and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam, 2006. [10] I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999.
  • [11] M. Eslami, Exact traveling wave solutions to the fractional coupled nonlinear Schrodinger equations, Applied Mathematics and Computation, Vol. 285, (2016), 141-148.
  • [12] R. Khalil, M. Al Horani, A. Yousef and M. Sababheh, A new definition of fractional derivative, Journal of Computational and Applied Mathematics, Vol. 264, (2014), 65-70.
  • [13] S.G. Samko, A.A. Kilbas, and O.I. Marichev, Fractional Integrals and Derivatives. Theory and Applications. Gordon and Breach, Yverdon, 1993.
  • [14] M. Yavuz, T. A. Sulaiman, F. Usta and H. Bulut, Analysis and numerical computations of the fractional regularized long-wave equation with damping term, Math Meth Appl Sci., (2020), 1–18.
  • [15] M. Z. Sarikaya and F. Usta, On Comparison Theorems for Conformable Fractional Differential Equations, Int. J. Anal. Appl., Vol. 12, No. 2 (2016), 207-214.
  • [16] F. Usta and M. Z. Sarıkaya, The analytical solution of Van der Pol and Lienard differential equations within conformable fractional operator by retarded integral inequalities, Demonstratio Mathematica, Vol. 52, No. 1 (2019), 204-212.
  • [17] F. Usta, Numerical analysis of fractional Volterra integral equations via Bernstein approximation method, Journal of Computational and Applied Mathematics, Vol. 384, (2021), 113198.
  • [18] F. Usta, Fractional Type Poisson Equations By Radial Basis Functions Kansa Approach, Journal of Inequalities and Special Functions, Vol. 7 No. 4 (2016), 143-149.
  • [19] F. Usta, Numerical solution of fractional elliptic PDE’s by the collocation method, Applications and Applied Mathematics: An International Journal (AAM), Vol. 12, No. 1 (2017), 470-478.
  • [20] F. Usta, A mesh free technique of numerical solution of newly defined conformable differential equations, Konuralp Journal of Mathematics, Vol. 4, No. 2 (2016), 149-157.
  • [21] F. Usta, H. Budak, M. Z. Sarıkaya, Yang-Laplace transform method Volterra and Abel’s integro-differential equations of fractional order, International Journal of Nonlinear Analysis and Applications, Vol. 9, No.2 (2018), 203-214.
  • [22] F. Usta, A conformable calculus of radial basis functions and its applications, An In- ternational Journal of Optimization and Control: Theories and Applications (IJOCTA), Vol.8, No.2 (2018), 176-182.

Time Fractional Diffusion Equation with Periodic Boundary Conditions

Yıl 2020, Cilt: 8 Sayı: 2, 337 - 342, 27.10.2020

Süleyman Çetinkaya Ali Demir

Öz

The aim of this research is to establish the analytic solution of time fractional diffusion equations with periodic boundary conditions in one dimension by implementing well-known separation of variables method. First, the eigenvalues of the obtained Sturm-Liouville problem are determined by investigating all cases. The corresponding eigenfunctions are obtained in the second step. Utilizing eigenvalues and eigenfunctions, the Fourier series of the solution is constructed in terms of Mittag-Leffler function and the coefficients are computed by taking $L^2$ inner product and initial condition into account at the final step.

Anahtar Kelimeler

Caputo fractional derivative Mittag-Leffler function Periodic boundary conditions Spectral method Time-fractional diffusion equation

Kaynakça

  • [1] A. Demir, M. A. Bayrak and E. Ozbilge, New approaches for the solution of space-time fractional Schr¨odinger equation, Advances in Difference Equation, Vol. 2020:133, (2020).
  • [2] A. Demir and M. A. Bayrak, A New Approach for the Solution of Space-TimeFractional Order Heat-Like Partial Differential Equations by Residual Power Series Method, Communications in Mathematics and Applications, Vol. 10, No. 3 (2019), 585–597.
  • [3] A. Demir, M. A. Bayrak and E. Ozbilge, A New Approach for the Approximate AnalyticalSolution of Space-Time Fractional Differential Equations by the Homotopy Analysis Method, Advances in Mathematical Physics, Vol. 2019, Article ID 5602565, (2019).
  • [4] A. Demir, M. A. Bayrak and E. Ozbilge, An Approximate Solution of the Time-Fractional FisherEquation with Small Delay by Residual Power Series Method, Mathematical Problems in Engineering, Vol. 2018, Article ID 9471910, (2018).
  • [5] S. Cetinkaya, A. Demir and H. Kodal Sevindir, The analytic solution of initial boundary value problem including time-fractional diffusion equation, Facta Universitatis Ser. Math. Inform, Vol. 35, No. 1 (2020), 243-252.
  • [6] S. Cetinkaya, A. Demir, and H. Kodal Sevindir, The analytic solution of sequential space-time fractional diffusion equation including periodic boundary conditions, Journal of Mathematical Analysis, Vol. 11, No.1 (2020), 17-26.
  • [7] S. Cetinkaya and A. Demir, The Analytic Solution of Time-Space Fractional Diffusion Equation via New Inner Product with Weighted Function, Communications in Mathematics and Applications, Vol. 10, No. 4 (2019), 865-873.
  • [8] S. Cetinkaya, A. Demir, and H. Kodal Sevindir, The Analytic Solution of Initial Periodic Boundary Value Problem Including Sequential Time Fractional Diffusion Equation, Communications in Mathematics and Applications, Vol. 11, No. 1 (2020), 173-179.
  • [9] A. A. Kilbas, H. M. Srivastava and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam, 2006. [10] I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999.
  • [11] M. Eslami, Exact traveling wave solutions to the fractional coupled nonlinear Schrodinger equations, Applied Mathematics and Computation, Vol. 285, (2016), 141-148.
  • [12] R. Khalil, M. Al Horani, A. Yousef and M. Sababheh, A new definition of fractional derivative, Journal of Computational and Applied Mathematics, Vol. 264, (2014), 65-70.
  • [13] S.G. Samko, A.A. Kilbas, and O.I. Marichev, Fractional Integrals and Derivatives. Theory and Applications. Gordon and Breach, Yverdon, 1993.
  • [14] M. Yavuz, T. A. Sulaiman, F. Usta and H. Bulut, Analysis and numerical computations of the fractional regularized long-wave equation with damping term, Math Meth Appl Sci., (2020), 1–18.
  • [15] M. Z. Sarikaya and F. Usta, On Comparison Theorems for Conformable Fractional Differential Equations, Int. J. Anal. Appl., Vol. 12, No. 2 (2016), 207-214.
  • [16] F. Usta and M. Z. Sarıkaya, The analytical solution of Van der Pol and Lienard differential equations within conformable fractional operator by retarded integral inequalities, Demonstratio Mathematica, Vol. 52, No. 1 (2019), 204-212.
  • [17] F. Usta, Numerical analysis of fractional Volterra integral equations via Bernstein approximation method, Journal of Computational and Applied Mathematics, Vol. 384, (2021), 113198.
  • [18] F. Usta, Fractional Type Poisson Equations By Radial Basis Functions Kansa Approach, Journal of Inequalities and Special Functions, Vol. 7 No. 4 (2016), 143-149.
  • [19] F. Usta, Numerical solution of fractional elliptic PDE’s by the collocation method, Applications and Applied Mathematics: An International Journal (AAM), Vol. 12, No. 1 (2017), 470-478.
  • [20] F. Usta, A mesh free technique of numerical solution of newly defined conformable differential equations, Konuralp Journal of Mathematics, Vol. 4, No. 2 (2016), 149-157.
  • [21] F. Usta, H. Budak, M. Z. Sarıkaya, Yang-Laplace transform method Volterra and Abel’s integro-differential equations of fractional order, International Journal of Nonlinear Analysis and Applications, Vol. 9, No.2 (2018), 203-214.
  • [22] F. Usta, A conformable calculus of radial basis functions and its applications, An In- ternational Journal of Optimization and Control: Theories and Applications (IJOCTA), Vol.8, No.2 (2018), 176-182.
Toplam 21 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Articles
Yazarlar

Süleyman Çetinkaya

Ali Demir

Yayımlanma Tarihi 27 Ekim 2020
Gönderilme Tarihi 10 Haziran 2020
Kabul Tarihi 8 Ekim 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 8 Sayı: 2

Kaynak Göster

APA Çetinkaya, S., & Demir, A. (2020). Time Fractional Diffusion Equation with Periodic Boundary Conditions. Konuralp Journal of Mathematics, 8(2), 337-342.
AMA Çetinkaya S, Demir A. Time Fractional Diffusion Equation with Periodic Boundary Conditions. Konuralp J. Math. Ekim 2020;8(2):337-342.
Chicago Çetinkaya, Süleyman, ve Ali Demir. “Time Fractional Diffusion Equation With Periodic Boundary Conditions”. Konuralp Journal of Mathematics 8, sy. 2 (Ekim 2020): 337-42.
EndNote Çetinkaya S, Demir A (01 Ekim 2020) Time Fractional Diffusion Equation with Periodic Boundary Conditions. Konuralp Journal of Mathematics 8 2 337–342.
IEEE S. Çetinkaya ve A. Demir, “Time Fractional Diffusion Equation with Periodic Boundary Conditions”, Konuralp J. Math., c. 8, sy. 2, ss. 337–342, 2020.
ISNAD Çetinkaya, Süleyman - Demir, Ali. “Time Fractional Diffusion Equation With Periodic Boundary Conditions”. Konuralp Journal of Mathematics 8/2 (Ekim 2020), 337-342.
JAMA Çetinkaya S, Demir A. Time Fractional Diffusion Equation with Periodic Boundary Conditions. Konuralp J. Math. 2020;8:337–342.
MLA Çetinkaya, Süleyman ve Ali Demir. “Time Fractional Diffusion Equation With Periodic Boundary Conditions”. Konuralp Journal of Mathematics, c. 8, sy. 2, 2020, ss. 337-42.
Vancouver Çetinkaya S, Demir A. Time Fractional Diffusion Equation with Periodic Boundary Conditions. Konuralp J. Math. 2020;8(2):337-42.
 Kapak Resmi İndir
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