Monotone Iterative Technique for Nonlinear Periodic Time Fractional Parabolic Problems

Abstract

In this paper, existence and uniqueness of weak solutions for a linear parabolic problem with conformable derivative are proved, the existence of weak periodic solutions for conformable fractional parabolic nonlinear dierential equation is proved by using a more generalized monotone iterative method combined with the method of upper and lower solutions. We prove the convergence of monotone sequence to weak periodic minimal and maximal solutions. Moreover, the conformable version of the Lions-Magness and AubinLions lemmas are also proved.

On dynamics of fractional incommensurate model of Covid-19 with nonlinear saturated incidence rate

“…where L 1 is defined in (4). Similar results for the kernels G 2 , G 3 , G 4 , and G 5 can be obtained using…”

“…We mention them Riemann-Liouville derivative, Caputo derivative, Riesz derivative, Grünwald-Letnikov derivative, Hadamard derivative, Marchaud derivative, Weyl derivative and recently, other types of fractional derivative have appeared, the most important of which are Caputo-Fabrizio derivative and Atangana-Baleanu derivative, the latter has aroused the interest of many researchers in various fields, due to its efficiency in modeling real problems in several areas, namely epidemiological problems. In recent years researchers have been interested in studying some real problems in various fields using fractional calculus , such as physical problems [1,3,4], engineering mechanics [5], epidemiological models [6,7,8,9,10], image processing [11,12], chaos theory [13,14] and others.…”