Wellposed results for nonlocal fractional parabolic equation involving CaputoFabrizio operator
Volume 26, Issue 4, pp 357367
http://dx.doi.org/10.22436/jmcs.026.04.04
Publication Date: January 06, 2022
Submission Date: September 18, 2021
Revision Date: October 19, 2021
Accteptance Date: November 05, 2021
Authors
T. T. Phong
 Division of Applied Mathematic, Thu Dau Mot University, Binh Duong province, Viet Nam.
L. D. Long
 Division of Applied Mathematic, Thu Dau Mot University, Binh Duong province, Viet Nam.
Abstract
In this paper, we study the parabolic problem associated with nonlocal conditions, with the CaputoFabrizio derivative. Equations on the sphere have many important applications in physics, phenomena, and oceanography. The main motivation for us to study nonlocal boundary value problems comes from two main reasons: the first reason is that
current major interest in several application areas. The second reason is to study approximation for the terminal value problem.
With some given data, we prove that the problem has only the solution for two cases. In case \(\epsilon = 0,\) we prove the problem has a local solution. In case \(\epsilon > 0,\) then the problem has a global solution. The main tools and techniques in our demonstration are
of using Banach's fixed point theorem in conjunction with some Fourier series analysis involved some evaluation of spherical harmonic function.
Several upper and lower upper limit techniques for the MittagLefler functions are also applied.
Share and Cite
ISRP Style
T. T. Phong, L. D. Long, Wellposed results for nonlocal fractional parabolic equation involving CaputoFabrizio operator, Journal of Mathematics and Computer Science, 26 (2022), no. 4, 357367
AMA Style
Phong T. T., Long L. D., Wellposed results for nonlocal fractional parabolic equation involving CaputoFabrizio operator. J Math Comput SCIJM. (2022); 26(4):357367
Chicago/Turabian Style
Phong, T. T., Long, L. D.. "Wellposed results for nonlocal fractional parabolic equation involving CaputoFabrizio operator." Journal of Mathematics and Computer Science, 26, no. 4 (2022): 357367
Keywords
 Nonlocal parabolic equation
 Banach fixed point theory
 sphere
 regularity
MSC
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