Time Fractional Equation with Non-homogenous Dirichlet Boundary Conditions
Time Fractional Equation with Non-homogenous Dirichlet Boundary Conditions
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.
Keywords:
Caputo fractional derivative, Time-fractional diffusion equation, Mittag-Leffler function Initial-boundary-value problems, Spectral method,
___
- 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.
- Yayın Aralığı: Yılda 6 Sayı
- Başlangıç: 1997
- Yayıncı: Sakarya Üniversitesi