The Analytic Solution of Initial Periodic Boundary Value Problem Including Sequential Time Fractional Diffusion Equation
In this study, the separation of variables method is applied to form the analytic solution of periodic boundary value problem including time fractional differential equation with periodic boundary conditions in one dimension. The solution is obtained in the form of a Fourier series with respect to the eigenfunctions of a corresponding Sturm-Liouville eigenvalue problem.
M. A. Bayrak and A. Demir, A new approach for space-time fractional partial differential equations by Residual power series method, Applied Mathematics and Computation 336 (2013), 215 – 230, DOI: 10.1016/j.amc.2018.04.032.
M. A. Bayrak and A. Demir, Inverse problem for determination of an unknown coefficient in the time fractional diffusion equation, Communications in Mathematics and Applications 9 (2018), 229 – 237, DOI: 10.26713/cma.v9i2.722.
E. Ozbilge and A. Demir, Analysis of the inverse problem in a time fractional parabolic equation with mixed boundary conditions Boundary Value Problems 2014 (2014), article number 134, DOI: 10.1186/1687-2770-2014-134.
A. Demir, F. Kanca and E. Ozbilge, Numerical solution and distinguishability in time fractional parabolic equation, Boundary Value Problems 2015 (2015), article number 142, DOI: 10.1186/s13661-015-0405-6.
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 Mathematichal 2019 (2019), article ID 5602565, DOI: 10.1155/2019/5602565.
A. Demir, S. Erman, B. Özgür and E. Korkmaz, Analysis of fractional partial differential equations by Taylor series expansion, Boundary Value Problems 2013 (2013), article number 68, DOI: 10.1186/1687-2770-2013-68.
S. Erman and A. Demir, A novel approach for the stability analysis of state dependent differential equation, Communications in Mathematics and Applications 7 (2016), 105 – 113, DOI: 10.26713/cma.v7i2.373.
F. Huang and F. Liu, The time-fractional diffusion equation and fractional advection-dispersion equation, The ANZIAM Journal 46 (2005), 1 – 14, DOI: 10.1017/S1446181100008282.
A. A. Kilbas, H. M. Srivastava and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam (2006), https://books.google.co.in/books?hl=en&lr=&id=LhkO83ZioQkC&oi=fnd&pg=PA1&ots=fhdR7ftSNL&sig=2jwea6g7lGWpABIzkmWp2DiFnjo&redir_esc=y#v=onepage&q&f=false.
Y. Luchko, Initial boundary value problems for the one dimensional time-fractional diffusion equation, Fractional Calculus and Applied Analysis 15 (2012), 141 – 160, DOI: 10.2478/s13540-012-0010-7.
Y. Luchko, Initial-boundary-value problems for the generalized multi-term time-fractional diffusion equation, Journal of Mathematical Analysis and Applications 74 2 (2011), 538 – 548, DOI: 10.1016/j.jmaa.2010.08.048.
S. Momani and Z. Odibat, Numerical comparison of methods for solving linear differential equations of fractional order, Chaos, Solitons and Fractals 31(5) (2007), 1248 – 1255, DOI: 10.1016/j.chaos.2005.10.068.
B. Ozgur and A. Demir, Some stability charts of a neural field model of two neural populations, Communications in Mathematics and Applications 7 (2016), 159 – 166, DOI: 10.26713/cma.v7i2.481.
L. Plociniczak, Analytical studies of a time-fractional porous medium equation. Derivation, approximation and applications, Communications in Nonlinear Science and Numerical Simulation 24(1-3) (2015), 169 – 183, DOI: 10.1016/j.cnsns.2015.01.005.
I. Podlubny, Fractional Differential Equations, Academic Press, San Diego (1999), https://lib.ugent.be/catalog/rug01:002178612.
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