Perturbation Results and Monotone Iterative Technique for Fractional Evolution Equations - Jia Mu (Abstract and Applied Analysis)
We mainly study the fractional evolution equation in an ordered Banach space 𝑋𝐶𝐷𝑎0+𝑢(𝑡)+𝐴𝑢(𝑡)=𝑓(𝑡,𝑢(𝑡),𝐺𝑢(𝑡)) , 1<𝛼<2, 𝑢(0)=𝑥∈𝑋, 𝑢(0)=𝜃. Using the monotone iterative technique based on lower and upper solutions, the existence and uniqueness results are obtained. The necessary perturbation results for accomplishing this approach are also developed.