Abstract
In this paper, the existence and uniqueness of the weak solution for a linear parabolic equation with conformable derivative are proved, the existence of weak periodic solutions for conformable fractional parabolic nonlinear differential equation is proved by using a more generalized monotone iterative method combined with the method of upper and lower solutions. We prove the monotone sequence converge to weak periodic minimal and maximal solutions. Moreover, the conformable version of the Lions-Magness and Aubin–Lions lemmas are also proved.
Highlights
IntroductionBinh et al [12] have considered the initial inverse problem for a diusion equation with a conformable derivative in a general bounded domain
Let Ω ⊂ RN be a bounded domain with boundary ∂Ω, Q = (0, T ) × Ω and Γ = [0, T ] × ∂Ω In this paper, we consider the following fractional parabolic periodic boundary valued problem (PBVP for short)Received July 25, 2020, Accepted: September 5, 2020, Online: September 14, 2020.A
In this paper we develop the generalized monotone iterative method combined with the method of upper and lower solutions for the nonlinear fractional periodic parabolic dierential problems
Summary
Binh et al [12] have considered the initial inverse problem for a diusion equation with a conformable derivative in a general bounded domain. Au et al [10] studied the ill-posed property in the sense of Hadamard for an inverse nonlinear diusion equation with conformable time derivative. In this paper we develop the generalized monotone iterative method combined with the method of upper and lower solutions for the nonlinear fractional periodic parabolic dierential problems. We show that the monotone sequences, which are solutions of the linear fractional parabolic equation converge to the minimal and maximal periodic solutions of the nonlinear equation, these comparison results are used to establish the last result.
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