Some existence results on nonlinear fractional differential equations

Abstract

In this paper, by using fixed-point methods, we study the existence and uniqueness of a solution for the nonlinear fractional differential equation boundaryvalue problem D α u(t) = f (t, u(t)) with a RiemannLiouville fractional derivative via the different boundary-value problems u(0) = u(T), and the threepoint boundary condition u(0) = β 1 u(η) and u(T) = β 2 u(η), where T > 0, t ∈ I = [0, T], 0 < α < 1, 0 < η < T, 0 < β 1 < β 2 < 1.

New fixed point results in rectangular metric space and application to fractional calculus

“…Here we give an application of Corollary 1 which guarantees the existence of solution for a nonlinear fractional differential equation considered in [2] (see also ([5]). We will study the existence of solutions for the nonlinear fractional differential equation:…”

Coincidence Points of a Sequence of Multivalued Mappings in Metric Space with a Graph

“…In the next result, we discussed the generalization of fractional differential equation described in [21]. For the closed interval I = [0, 1] , assume function g ∈ C (I, R) and f : I × R → R is a continuous function.…”

Existence results for three-point boundary value problems for nonlinear fractional differential equations

“…The increasing interest of fractional differential equations and inclusions are motivated by their applications in various fields of science such as physics, chemistry, engineering, biology, economics, fluid mechanics, control theory, etc. For this reason, in the recent years, many papers have been published about fractional differential equations and inclusions by mathematicians and other researchers (for example, see [1,2,4,5,6,7,8,9,12,16,17,18,19,22] and the references therein).…”