Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4620458 | Journal of Mathematical Analysis and Applications | 2009 | 12 Pages |
Abstract
We prove the existence-uniqueness of the solution to the nonlinear n-term time-fractional differential equation with constant coefficients in the Banach space C([0,T]),(1)b0Dβ0u(t)+âi=1mâ1biDβiu(t)+âi=mnâ1biDαiu(t)+bnDαnu(t)=f(t,u(t)),tâ(0,T),xâR,u(0)=f(0),ut(0)=g(0),0<β1<β2<â¯<βmâ1<1<αm<αm+1<â¯<αn<2(respectively 0<β1<â¯<βmâ1<αm<αm+1<â¯<αn<1,1<β1<â¯<βmâ1<αm<αm+1<â¯<αn<2), f(t,u(t))âC([0,T)ÃC([0,T))) is a given function meant to be composed with a real valued function u and satisfies Assumption 1.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Mirjana StojanoviÄ,