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### Solution of hybrid time fractional diffusion problem via weighted inner product

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Języki publikacji
EN
Abstrakty
EN
In this research, we discuss the construction of the analytic solution of homogenous initial boundary value problem including partial differential equations of fractional order. Since the homogenous initial boundary value problem involves the Hybrid fractional order derivative with various coefficients functions, it has classical initial and boundary conditions. By means of separation of the variables method and the inner product defined on L 2 [0,l], the solution is constructed in the form of a Fourier series including the bivariate Mittag-Leffler function. An illustrative example presents the applicability and influence of the separation of variables method on time fractional diffusion problems. Moreover, as the fractional order α tends to 1, the solution of the fractional diffusion problem tends to the solution of the diffusion problem which proves the accuracy of the solution.
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EN
PL
Rocznik
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17--27
Opis fizyczny
Bibliogr. 21 poz. rys.
Twórcy
autor
• Faculty of Arts and Sciences, Kocaeli University Kocaeli, Turkey
autor
• Faculty of Arts and Sciences, Kocaeli University Kocaeli, Turkey
Bibliografia
• [1] Baleanu, D., Fernandez, A., & Akgul, A. (2020). On a fractional operator combining proportional and classical differintegrals. Mathematics, 8(360).
• [2] Sweilam, N.H., Al-Mekhlafi, S.M., & Baleanu, D. (2020). A hybrid fractional optimal control for a novel Coronavirus (2019-nCov) mathematical model. Journal of Advanced Research, DOI: 10.1016/j.jare.2020.08.006.
• [3] Sweilam, N.H., Al-Mekhlafi, S.M., Almutairi, A., & Baleanu, D. (2021). A hybrid fractional COVID-19 model with general population mask use: Numerical treatments. Alexandria Engineering Journal, 60(3), 3219-3232.
• [4] Ibrahim, R.W., & Baleanu, D. (2021). On quantum hybrid fractional conformable differential and integral operators in a complex domain. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 115, 31, DOI: 10.1007/s13398-020-00982-5.
• [5] Aslam, M., Murtaza, R., Khan, H., Baleanu, D., & Khan, A. (2020). Singular hybrid fractional differential systems. Authorea, DOI: 10.22541/au.158480068.83814487.
• [6] Fernandez, A., Kürt, C., & Özarslan, M.A. (2020). A naturally emerging bivariate Mittag-Leffler function and associated fractional-calculus operators. Computational and Applied Mathematics, 39, Article number: 200(2020).
• [7] Asjad, M.I., Ikram, M.D., Ali, R., Baleanu, D., & Alshomrani, A.S. (2020). New analytical solutions of heat transfer flow of clay-water base nanoparticles with the application of novel hybrid fractional derivative. Thermal Science, 24(Suppl. 1), 343-350.
• [8] Chu, Y.M., Khan, U., Ahmed, N., Mohyud-Din, S.T., & Khan, I. (2020). Heat and mass transport investigation in radiative and chemically reacting fluid over a differentially heated surface and internal heating. Open Physics, DOI: 10.1515/phys-2020-0182.
• [9] Geng, F., & Wu, X. (2021). Kernel functions-based approach for distributed order diffusion equations. Numerical Methods for Partial Differential Equations, 37, 1269-1281.
• [10] Ikram, M.D., Asjad, M.I., Akgül, A., & Baleanu, D. (2021). Effects of hybrid nanofluid on novel fractional model of heat transfer flow between two parallel plates. Alexandria Engineering Journal, 60(4), 3593-3604.
• [11] Günerhan, H., Dutta, H. Dokuyucu, M.A., & Adel, W. (2020). Analysis of a fractional HIV model with Caputo and constant proportional Caputo operators. Chaos, Solitons & Fractals, 139, 110053.
• [12] Acay, B., & Inc, M. (2021). Fractional modeling of temperature dynamics of a building with singular kernels. Chaos, Solitons & Fractals, 142, 110482.
• [13] Asjad, M.I. (2020). Novel fractional differential operator and its application in fluid dynamics. Journal of Prime Research in Mathematics, 16(2), 67-79.
• [14] Ahmad, M., Imran, M.A., Baleanu, D., & Alshomrani, A.S. (2020). Thermal analysis of magnetohydrodynamic viscous fluid with innovative fractional derivative. Thermal Science, 24(Supp. 1), 351-359.
• [15] 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, 011109.
• [16] 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), 243-252.
• [17] 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), 865-873.
• [18] Cetinkaya, S., & Demir, A. (2020). Time fractional diffusion equation with periodic boundary conditions. Konuralp Journal of Mathematics, 8(2), 337-342.
• [19] Cetinkaya, S., & Demir, A. (2020). Time fractional equation including non-homogenous Dirichlet boundary conditions. Sakarya University Journal of Science, 24(6), 1185-1190.
• [20] Naber, M. (2004). Distributed order fractional sub-diffusion. Fractals, 12(1), 23-32.
• [21] Fernandez, A., Kurt, C., & Ozarslan, M.A. (2020). A naturally emerging bivariate Mittag-Leffler function and associated fractional-calculus operators. Computational and Applied Mathematics, 39(200)
Uwagi
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).
Typ dokumentu
Bibliografia