Cauchy problem for inhomogeneous fractional nonclassical diffusion equation on the sphere
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Authors
L. D. Long
- Division of Applied Mathematic, Thu Dau Mot University, Binh Duong province, Viet Nam.
Abstract
Pseudo-parabolic equation on spheres have many important applications in physical
phenomena, oceanography and meteorology, geophysics. The main purpose of this paper is to prove
the existence and unique solution of the nonlinear pseudo-parabolic equation on the sphere. To
do this, we used some analysis of Fourier series associated with several evaluations of the
spherical harmonics function. Some of the upper and lower bounds of the Mittag-Lefler functions are also used. This result is one of the first studies of fractional nonclassical diffusion equation on
the sphere.
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ISRP Style
L. D. Long, Cauchy problem for inhomogeneous fractional nonclassical diffusion equation on the sphere, Journal of Mathematics and Computer Science, 25 (2022), no. 4, 303--311
AMA Style
Long L. D., Cauchy problem for inhomogeneous fractional nonclassical diffusion equation on the sphere. J Math Comput SCI-JM. (2022); 25(4):303--311
Chicago/Turabian Style
Long, L. D.. "Cauchy problem for inhomogeneous fractional nonclassical diffusion equation on the sphere." Journal of Mathematics and Computer Science, 25, no. 4 (2022): 303--311
Keywords
- Fractional diffusion equation
- Riemman-Liouville
- regularity
MSC
References
-
[1]
K. A. Abro, A. Atangana, Mathematical analysis of memristor through fractal‐fractional differential operators: a numerical study, Math. Methods Appl. Sci., 43 (2020), 6378--6395
-
[2]
A. Atangana, A. Akgül, K. M. Owolabi, Analysis of fractal fractional differential equations, Alexandria Eng. J., 59 (2020), 1117--1134
-
[3]
A. Atangana, E. Bonyah, Fractional stochastic modeling: New approach to capture more heterogeneity, Chaos, 29 (2019), 13 pages
-
[4]
A. Atangana, E. F. D. Goufo, Cauchy problems with fractal-fractional operators and applications to groundwater dynamics, Fractals, 28 (2020), 21 pages
-
[5]
A. Atangana, Z. Hammouch, Fractional calculus with power law: The cradle of our ancestors, Eur. Phys. J. Plus, 134 (2019), 13 pages
-
[6]
Z. Brzeźniak, B. Goldys, Q. T. Le Gia, Random attractors for the stochastic Navier-Stokes equations on the 2D unit sphere, J. Math. Fluid Mech., 20 (2018), 227--253
-
[7]
R. M. Ganji, H. Jafari, S. Nemati, A new approach for solving integro-differential equations of variable order, J. Comput. Appl. Math., 379 (2020), 13 pages
-
[8]
H. Jafari, H. Tajadodi, R. M. Ganji, A numerical approach for solving variable order differential equations based on Bernstein polynomials, Comput. Math. Methods, 1 (2019), 11 pages
-
[9]
S. Kumar, A. Atangana, A numerical study of the nonlinear fractional mathematical model of tumor cells in presence of chemotherapeutic treatment, Int. J. Biomath., 13 (2020), 17 pages
-
[10]
Q. T. Le Gia, Galerkin approximation of elliptic PDEs on spheres, J. Approx. Theory, 130 (2004), 125--149
-
[11]
Q. T. Le Gia, Approximation of parabolic PDEs on spheres using collocation method, Adv. Comput. Math., 22 (2005), 377--397
-
[12]
Q. T. Le Gia, I. H. Sloan, T. Tran, Overlapping additive Schwarz preconditioners for elliptic PDEs on the unit sphere, Math. Comp., 78 (2009), 79--101
-
[13]
Q. T. Le Gia, N. H. Tuan, T. Tran, Solving the backward heat equation on the unit sphere, ANZIAM J. Electron. Suppl., 56 (2014), 262--278
-
[14]
N. H. Luc, H. Jafari, P. Kumam, N. H. Tuan, On an initial value problem for time fractional pseudo‐parabolic equation with Caputo derivarive, Mathematical Methods in the Applied Sciences, 2021 (2021), to appear
-
[15]
J. Manimaran, L. Shangerganesh, A. Debbouche, A time-fractional competition ecological model with cross-diffusion, Math. Methods Appl. Sci., 43 (2020), 5197--5211
-
[16]
J. Manimaran, L. Shangerganesh, A. Debbouche, Finite element error analysis of a time-fractional nonlocal diffusion equation with the Dirichlet energy, J. Comput. Appl. Math., 382 (2021), 11 pages
-
[17]
T. B. Ngoc, T. Caraballo, N. H. Tuan, Y. Zhou, Existence and regularity results for terminal value problem for nonlinear super-diffusive fractional wave equations, Nonlinearity, 34 (2021), 12 pages
-
[18]
T. B. Ngoc, Y. Zhou, D. O'Regan, N. H. Tuan, On a terminal value problem for pseudoparabolic equations involving Riemann-Liouville fractional derivatives, Appl. Math. Lett., 106 (2020), 9 pages
-
[19]
O. Nikan, H. Jafari, A. Golbabai, Numerical analysis of the fractional evolution model for heat flow in materials with memory, Alexandria Eng. J., 59 (2020), 2627--2637
-
[20]
C. V. Pao, Reaction diffusion equations with nonlocal boundary and nonlocal initial conditions, J. Math. Anal. Appl., 195 (1995), 702--718
-
[21]
N. D. Phuong, N. H. Luc, Note on a Nonlocal Pseudo-Parabolic Equation on the Unit Sphere, Dyn. Syst. Appl., 30 (2021), 295--304
-
[22]
I. Podlubny, Fractional Differential Equations, Academic Press, San Diego (1999)
-
[23]
M. Ruzhansky, N. Tokmagambetov, B. T. Torebek, On a non-local problem for a multi-term fractional diffusion-wave equation, Fract. Calc. Appl. Anal., 23 (2020), 324--355
-
[24]
K. Sakamoto, M. Yamamoto, Initial value/boundary value problems for fractional diffusion-wave equations and applications to some inverse problems, J. Math. Anal. Appl., 382 (2011), 426--447
-
[25]
N. H. Sweilam, S. M. Al-Mekhlafi, T. Assiri, A. Atangana, Optimal control for cancer treatment mathematical model using Atangana–Baleanu–Caputo fractional derivative, Adv. Difference Equ., 2020 (2020), 21 pages
-
[26]
N. H. Tuan, A. Debbouche, T. B. Ngoc, Existence and regularity of final value problems for time fractional wave equations, Comput. Math. Appl., 78 (2019), 1396--1414
-
[27]
N. H. Tuan, L. N. Huynh, T. B. Ngoc, Y. Zhou, On a backward problem for nonlinear fractional diffusion equations, Appl. Math. Lett., 92 (2019), 76--84
-
[28]
N. H. Tuan, Y. Zhou, T. N. Thach, N. H. Can, Initial inverse problem for the nonlinear fractional Rayleigh-Stokes equation with random discrete data, Commun. Nonlinear Sci. Numer. Simul., 78 (2019), 18 pages