TY - JOUR
AU - Phong, T. T.
AU - Long, L. D.
PY - 2022
TI - Well-posed results for nonlocal fractional parabolic equation involving Caputo-Fabrizio operator
JO - Journal of Mathematics and Computer Science
SP - 357--367
VL - 26
IS - 4
AB - In this paper, we study the parabolic problem associated with non-local conditions, with the Caputo-Fabrizio derivative. Equations on the sphere have many important applications in physics, phenomena, and oceanography. The main motivation for us to study non-local 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 Mittag-Lefler functions are also applied.
SN - ISSN 2008-949X
UR - http://dx.doi.org/10.22436/jmcs.026.04.04
DO - 10.22436/jmcs.026.04.04
ID - Phong2022
ER -