Research Article
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Year 2020, Volume: 24 Issue: 6, 1185 - 1190, 01.12.2020
https://doi.org/10.16984/saufenbilder.749168

Abstract

References

  • A. Demir, M. A. Bayrak and E. Ozbilge, “New approaches for the solution of space-time fractional Schrödinger equation,” Advances in Difference Equation, vol. 2020, no.133, 2020.
  • 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, pp. 585–597, 2019.
  • A. Demir, M. A. Bayrak and E. Ozbilge, “A New Approach for the Approximate Analytical Solution of Space-Time Fractional Differential Equations by the Homotopy Analysis Method”, Advances in Mathematical Physics, vol. 2019, Article ID 5602565, 2019.
  • 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.
  • 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, pp. 243-252, 2020.
  • 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, pp. 17-26, 2020.
  • 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, pp. 865-873, 2019.
  • 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, pp. 173-179, 2020.
  • S. Cetinkaya and A. Demir, “Time Fractional Diffusion Equation with Periodic Boundary Conditions,” Konuralp Journal of Mathematics, vol. 8, no. 2, pp. 337-342, 2020.
  • A. A. Kilbas, H. M. Srivastava and J. J. Trujıllo, “Theory and Applications of Fractional Differential Equations,” Elsevier, Amsterdam, 2006.
  • I. Podlubny, “Fractional Differential Equations,” Academic Press, San Diego, 1999.

Time Fractional Equation with Non-homogenous Dirichlet Boundary Conditions

Year 2020, Volume: 24 Issue: 6, 1185 - 1190, 01.12.2020
https://doi.org/10.16984/saufenbilder.749168

Abstract

In this research, we discuss the construction of analytic solution of non-homogenous initial boundary value problem including PDEs of fractional order. Since non-homogenous initial boundary value problem involves Caputo fractional order derivative, it has classical initial and boundary conditions. By means of separation of variables method and the inner product defined on L^2 [0,l], the solution is constructed in the form of a Fourier series with respect to the eigenfunctions of a corresponding Sturm-Liouville eigenvalue problem including fractional derivative in Caputo sense used in this study. Illustrative example presents the applicability and influence of separation of variables method on fractional mathematical problems.

References

  • A. Demir, M. A. Bayrak and E. Ozbilge, “New approaches for the solution of space-time fractional Schrödinger equation,” Advances in Difference Equation, vol. 2020, no.133, 2020.
  • 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, pp. 585–597, 2019.
  • A. Demir, M. A. Bayrak and E. Ozbilge, “A New Approach for the Approximate Analytical Solution of Space-Time Fractional Differential Equations by the Homotopy Analysis Method”, Advances in Mathematical Physics, vol. 2019, Article ID 5602565, 2019.
  • 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.
  • 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, pp. 243-252, 2020.
  • 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, pp. 17-26, 2020.
  • 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, pp. 865-873, 2019.
  • 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, pp. 173-179, 2020.
  • S. Cetinkaya and A. Demir, “Time Fractional Diffusion Equation with Periodic Boundary Conditions,” Konuralp Journal of Mathematics, vol. 8, no. 2, pp. 337-342, 2020.
  • A. A. Kilbas, H. M. Srivastava and J. J. Trujıllo, “Theory and Applications of Fractional Differential Equations,” Elsevier, Amsterdam, 2006.
  • I. Podlubny, “Fractional Differential Equations,” Academic Press, San Diego, 1999.
There are 11 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

Süleyman Çetinkaya 0000-0002-8214-5099

Ali Demir 0000-0003-3425-1812

Publication Date December 1, 2020
Submission Date June 9, 2020
Acceptance Date September 8, 2020
Published in Issue Year 2020 Volume: 24 Issue: 6

Cite

APA Çetinkaya, S., & Demir, A. (2020). Time Fractional Equation with Non-homogenous Dirichlet Boundary Conditions. Sakarya University Journal of Science, 24(6), 1185-1190. https://doi.org/10.16984/saufenbilder.749168
AMA Çetinkaya S, Demir A. Time Fractional Equation with Non-homogenous Dirichlet Boundary Conditions. SAUJS. December 2020;24(6):1185-1190. doi:10.16984/saufenbilder.749168
Chicago Çetinkaya, Süleyman, and Ali Demir. “Time Fractional Equation With Non-Homogenous Dirichlet Boundary Conditions”. Sakarya University Journal of Science 24, no. 6 (December 2020): 1185-90. https://doi.org/10.16984/saufenbilder.749168.
EndNote Çetinkaya S, Demir A (December 1, 2020) Time Fractional Equation with Non-homogenous Dirichlet Boundary Conditions. Sakarya University Journal of Science 24 6 1185–1190.
IEEE S. Çetinkaya and A. Demir, “Time Fractional Equation with Non-homogenous Dirichlet Boundary Conditions”, SAUJS, vol. 24, no. 6, pp. 1185–1190, 2020, doi: 10.16984/saufenbilder.749168.
ISNAD Çetinkaya, Süleyman - Demir, Ali. “Time Fractional Equation With Non-Homogenous Dirichlet Boundary Conditions”. Sakarya University Journal of Science 24/6 (December 2020), 1185-1190. https://doi.org/10.16984/saufenbilder.749168.
JAMA Çetinkaya S, Demir A. Time Fractional Equation with Non-homogenous Dirichlet Boundary Conditions. SAUJS. 2020;24:1185–1190.
MLA Çetinkaya, Süleyman and Ali Demir. “Time Fractional Equation With Non-Homogenous Dirichlet Boundary Conditions”. Sakarya University Journal of Science, vol. 24, no. 6, 2020, pp. 1185-90, doi:10.16984/saufenbilder.749168.
Vancouver Çetinkaya S, Demir A. Time Fractional Equation with Non-homogenous Dirichlet Boundary Conditions. SAUJS. 2020;24(6):1185-90.