Yıl: 2020 Cilt: 3 Sayı: 2 Sayfa Aralığı: 59 - 63 Metin Dili: İngilizce DOI: 10.34088/kojose.797216 İndeks Tarihi: 14-02-2022

Equation Including Local Fractional Derivative and Neumann Boundary Conditions

Öz:
The aim of this study to discuss the construction of solution of fractional partial differential equations (FPDEs) with initial and boundary conditions. Since the homogenous initial boundary value problem involves local fractional-order derivative, it has classical initial and boundary conditions. By means of the separation of variables method (SVM) and the inner product on, we construct the solution in this series form in terms of eigenfunctions of related SturmLiouville problem. An illustrative example presents the applicability and influence of separation of variables method on fractional mathematical problems.
Anahtar Kelime:

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  • [1] Dumitru B., Arran F., Akgül A., 2020. On a Fractional Operator Combining Proportional and Classical Differintegrals. Mathematics, 8(360). doi:10.3390/math8030360
  • [2] Bisquert J., 2005. Interpretation of A Fractional Diffusion Equation with Nonconserved Probability Density in Terms of Experimental Systems with Trapping or Recombination. Physical Review E, 72. doi: 10.1103/PhysRevE.72.011109
  • [3] Ndolane S., 2019. Solutions of Fractional Diffusion Equations and Cattaneo-Hristov Diffusion Model. International Journal of Analysis and Applications, 17(2), pp. 191-207. doi: 10.28924/2291-8639-17-2019-191
  • [4] Aguilar J. F. G., Hernández M. M., 2014. Space-Time Fractional Diffusion-Advection Equation with Caputo Derivative. Abstract and Applied Analysis. 2014 doi: 10.1155/2014/283019
  • [5] Naber M., 2004. Distributed order fractional subdiffusion. Fractals, 12(1), pp. 23-32. doi: 10.1142/S0218348X04002410
  • [6] Nadal E., Abisset C. E., Cueto E., Chinesta F., 2018. On the Physical Interpretation of Fractional Diffusion. Comptes Rendus Mecanique, 346, pp. 581-589. doi: 10.1016/j.crme.2018.04.004
  • [7] Zhang W., Yi M., 2016. Sturm-Liouville Problem and Numerical Method of Fractional Diffusion Equation on Fractals. Advances in Difference Equations, 2016:217. doi: 10.1186/s13662-016-0945-9
  • [8] Cetinkaya S., Demir A., Kodal Sevindir H., 2020. The Analytic Solution of Initial Boundary Value Problem Including Time-fractional Diffusion Equation. Facta Universitatis Ser. Math. Inform, 35(1), pp. 243-252.
  • [9] Cetinkaya S., Demir A., Kodal Sevindir H., 2020. The Analytic Solution of Sequential Space-time Fractional Diffusion Equation Including Periodic Boundary Conditions. Journal of Mathematical Analysis, 11(1), pp. 17-26.
  • [10] Cetinkaya S., Demir A., 2019. The Analytic Solution of Time-Space Fractional Diffusion Equation via New Inner Product with Weighted Function. Communications in Mathematics and Applications, 10(4), pp. 865-873.
  • [11] Cetinkaya S., Demir A., Kodal Sevindir H., 2020. The Analytic Solution of Initial Periodic Boundary Value Problem Including Sequential Time Fractional Diffusion Equation. Communications in Mathematics and Applications, 11(1), pp. 173-179.
  • [12] Cetinkaya S., Demir A., Time Fractional Equation Including Non-homogenous Dirichlet Boundary Conditions. Sakarya University Journal of Science (Accepted Paper).
  • [13] Cetinkaya S., Demir A., Sequential Space Fractional Diffusion Equation's solutions via New Inner Product. Asian-European Journal of Mathematics (Accepted Paper). doi: 10.1142/S1793557121501217
  • [14] Cetinkaya S., Demir A., Time Fractional Diffusion Equation with Periodic Boundary Conditions. Konuralp Journal of Mathematics, 8(2), pp. 337-342.
APA ÇETINKAYA S, DEMİR A (2020). Equation Including Local Fractional Derivative and Neumann Boundary Conditions. , 59 - 63. 10.34088/kojose.797216
Chicago ÇETINKAYA SÜLEYMAN,DEMİR ALİ Equation Including Local Fractional Derivative and Neumann Boundary Conditions. (2020): 59 - 63. 10.34088/kojose.797216
MLA ÇETINKAYA SÜLEYMAN,DEMİR ALİ Equation Including Local Fractional Derivative and Neumann Boundary Conditions. , 2020, ss.59 - 63. 10.34088/kojose.797216
AMA ÇETINKAYA S,DEMİR A Equation Including Local Fractional Derivative and Neumann Boundary Conditions. . 2020; 59 - 63. 10.34088/kojose.797216
Vancouver ÇETINKAYA S,DEMİR A Equation Including Local Fractional Derivative and Neumann Boundary Conditions. . 2020; 59 - 63. 10.34088/kojose.797216
IEEE ÇETINKAYA S,DEMİR A "Equation Including Local Fractional Derivative and Neumann Boundary Conditions." , ss.59 - 63, 2020. 10.34088/kojose.797216
ISNAD ÇETINKAYA, SÜLEYMAN - DEMİR, ALİ. "Equation Including Local Fractional Derivative and Neumann Boundary Conditions". (2020), 59-63. https://doi.org/10.34088/kojose.797216
APA ÇETINKAYA S, DEMİR A (2020). Equation Including Local Fractional Derivative and Neumann Boundary Conditions. Kocaeli Journal of Science and Engineering, 3(2), 59 - 63. 10.34088/kojose.797216
Chicago ÇETINKAYA SÜLEYMAN,DEMİR ALİ Equation Including Local Fractional Derivative and Neumann Boundary Conditions. Kocaeli Journal of Science and Engineering 3, no.2 (2020): 59 - 63. 10.34088/kojose.797216
MLA ÇETINKAYA SÜLEYMAN,DEMİR ALİ Equation Including Local Fractional Derivative and Neumann Boundary Conditions. Kocaeli Journal of Science and Engineering, vol.3, no.2, 2020, ss.59 - 63. 10.34088/kojose.797216
AMA ÇETINKAYA S,DEMİR A Equation Including Local Fractional Derivative and Neumann Boundary Conditions. Kocaeli Journal of Science and Engineering. 2020; 3(2): 59 - 63. 10.34088/kojose.797216
Vancouver ÇETINKAYA S,DEMİR A Equation Including Local Fractional Derivative and Neumann Boundary Conditions. Kocaeli Journal of Science and Engineering. 2020; 3(2): 59 - 63. 10.34088/kojose.797216
IEEE ÇETINKAYA S,DEMİR A "Equation Including Local Fractional Derivative and Neumann Boundary Conditions." Kocaeli Journal of Science and Engineering, 3, ss.59 - 63, 2020. 10.34088/kojose.797216
ISNAD ÇETINKAYA, SÜLEYMAN - DEMİR, ALİ. "Equation Including Local Fractional Derivative and Neumann Boundary Conditions". Kocaeli Journal of Science and Engineering 3/2 (2020), 59-63. https://doi.org/10.34088/kojose.797216