Some existence results on nonlinear fractional differential equations

Baleanu, DumitruRezapour, ShahramMohammadi, Hakimeh2017-03-132017-03-132013Baleanu, D., Rezapour, S., Mohammadi, H. (2013). Some existence results on nonlinear fractional differential equations. Philosophical Transactions Of The Royal Society A-Mathematical Physical And Engineering Sciences, 371(1990). http://dx.doi.org/10.1098/rsta.2012.01441364-503Xhttp://hdl.handle.net/20.500.12416/1452In this paper, by using fixed-point methods, we study the existence and uniqueness of a solution for the nonlinear fractional differential equation boundary-value problem D(alpha)u(t) = f(t, u(t)) with a Riemann-Liouville fractional derivative via the different boundary-value problems u(0) = u(T), and the three-point boundary condition u(0)= beta(1)u(eta) and u(T) = beta(2)u(eta), where T > 0, t is an element of I = [0, T], 0 < alpha < 1, 0 < eta < T, 0 < beta(1) < beta(2) < 1.eninfo:eu-repo/semantics/closedAccessFractional CalculusCaputo Fractional DerivativeRiemann-Liouville Fractional DerivativeBoundary-Value ProblemSome existence results on nonlinear fractional differential equationsSome Existence Results on Nonlinear Fractional Differential EquationsArticle371199010.1098/rsta.2012.0144