Abstract
The Caputo conformable derivative is a new Caputo-type fractional differential operator generated by conformable derivatives. In this paper, using Banach fixed point theorem, we obtain the uniqueness of the solution of nonlinear and linear Cauchy problem with the conformable derivatives in the Caputo setting, respectively. We also establish two comparison principles and prove the extremal solutions for nonlinear fractional p -Laplacian differential system with Caputo conformable derivatives by utilizing the monotone iterative technique. An example is given to verify the validity of the results.
Highlights
IntroductionFractional calculus has been widely developed in pure mathematics and applied mathematics [1,2,3,4,5,6,7]
In recent years, fractional calculus has been widely developed in pure mathematics and applied mathematics [1,2,3,4,5,6,7].e characteristic of fractional calculus is that there are many different fractional derivatives or integrals, like Riemann–Liouville (RL), Caputo, Hadamard, Caputo–Hadamard types, and so on [1, 2, 8, 9]
It is well known that the monotone iterative technique coupled with the method of upper and lower solutions is an effective mechanism to obtain extremal solutions for nonlinear problems [15]
Summary
Fractional calculus has been widely developed in pure mathematics and applied mathematics [1,2,3,4,5,6,7]. It is well known that the monotone iterative technique coupled with the method of upper and lower solutions is an effective mechanism to obtain extremal solutions for nonlinear problems [15] By using this method, scholars have studied the periodic boundary value problems (BVPs) [16,17,18,19,20,21,22,23,24], anti-periodic BVPs [25,26,27], and integral BVPs [28, 29] of integer-order differential equations. The Caputo conformable fractional differential equations with the p-Laplacian operator have not been considered. Inspired by the above work, we study the nonlinear fractional p-Laplacian differential system involving the Caputo conformable derivatives as follows:.
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