[1] Hao, Y.J., Srivastava, H. M., Jafari, H., Yang, X.J., (2013), Helmholtz and di usion equations associated with local fractional derivative operators involving the Cantorian and Cantor-type cylindrical coordinates, Advances in Mathematical Physics, 2013, Article ID 754248, 1-5.
[2] Bisquert, J., (2005), Interpretation of a fractional diffusion equation with non-conserved probability density in terms of experimental systems with trapping or recombination, Physical Review E, 72(1), 011109.
[3] Sene, N., (2019), Solutions of Fractional Diffusion Equations and Cattaneo-Hristov Diffusion Model, International Journal of Analysis and Applications, 17(2), 191-207.
[4] Aguilar, J.F.G. and Hernández, M.M., (2014), Space-Time Fractional Diffusion-Advection Equation with Caputo Derivative, Abstract and Applied Analysis, 2014, Article ID 283019.
[5] Naber, M., (2004), Distributed order fractional sub-diffusion, Fractals, 12(1), 23-32.
[6] Nadal, E., Abisset-Chavanne, E., Cueto, E. and Chinesta, F., (2018), On the physical interpretation of fractional diffusion, Comptes Rendus Mecanique, 346, 581-589.
[7] Zhang, W. and Yi, M., (2016), Sturm-Liouville problem and numerical method of fractional diffusion equation on fractals, Advances in Difference Equations, 2016:217.
[8] Baleanu, D., Fernandez, A. and Akgül, A., (2020), On a Fractional Operator Combining Proportional and Classical Differintegrals, Mathematics, 8(360).
DIFFUSION EQUATION INCLUDING LOCAL FRACTIONAL DERIVATIVE AND 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 local fractional derivative, it has classical initial and boundary conditions. By means of separation of variables method and the inner product defined on 𝐿2[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 local fractional derivative used in this study. Illustrative example presents the applicability and influence of separation of variables method on fractional mathematical problems.
[1] Hao, Y.J., Srivastava, H. M., Jafari, H., Yang, X.J., (2013), Helmholtz and di usion equations associated with local fractional derivative operators involving the Cantorian and Cantor-type cylindrical coordinates, Advances in Mathematical Physics, 2013, Article ID 754248, 1-5.
[2] Bisquert, J., (2005), Interpretation of a fractional diffusion equation with non-conserved probability density in terms of experimental systems with trapping or recombination, Physical Review E, 72(1), 011109.
[3] Sene, N., (2019), Solutions of Fractional Diffusion Equations and Cattaneo-Hristov Diffusion Model, International Journal of Analysis and Applications, 17(2), 191-207.
[4] Aguilar, J.F.G. and Hernández, M.M., (2014), Space-Time Fractional Diffusion-Advection Equation with Caputo Derivative, Abstract and Applied Analysis, 2014, Article ID 283019.
[5] Naber, M., (2004), Distributed order fractional sub-diffusion, Fractals, 12(1), 23-32.
[6] Nadal, E., Abisset-Chavanne, E., Cueto, E. and Chinesta, F., (2018), On the physical interpretation of fractional diffusion, Comptes Rendus Mecanique, 346, 581-589.
[7] Zhang, W. and Yi, M., (2016), Sturm-Liouville problem and numerical method of fractional diffusion equation on fractals, Advances in Difference Equations, 2016:217.
[8] Baleanu, D., Fernandez, A. and Akgül, A., (2020), On a Fractional Operator Combining Proportional and Classical Differintegrals, Mathematics, 8(360).
S. Çetinkaya and A. Demir, “DIFFUSION EQUATION INCLUDING LOCAL FRACTIONAL DERIVATIVE AND NON-HOMOGENOUS DIRICHLET BOUNDARY CONDITIONS”, JSR-A, no. 045, pp. 101–110, December 2020.