Abstract:

We considered the nonlinear fractional differential equation^cD^α₀₊u(t)=f(t,u(t),u′(t)),a.e. t∈(0,1),u(0)=u′(1)=u″(0)=0,where ^cD^α₀₊ is the Caputo fractional order derivative, 2<α≤3 is a real number. We proved the existence of at least one solution of the boundary value problem using LeraySchauder continuation principle.

Key words: fractional differential equation, Carathéodory conditions, priori estimate, LeraySchauder continuation principle