A higher-order nonlocal three-point boundary value problem of sequential fractional differential equations. (English) Zbl 1324.34002

Ahmad, Bashir; Ntouyas, Sotiris K.

Miskolc Math. Notes 15, No. 2, 265-278 (2014).

Summary: This paper investigates the existence of solutions for a sequential fractional differential equation of arbitrary order \(\xi + 1, ~\xi \in (n-1, n], ~n \geq 2\) with three-point nonlocal boundary conditions. We make use of standard tools of fixed point theory to establish our existence results. An illustrative example and some special cases are also discussed.

MSC:

34A08	Fractional ordinary differential equations
34B15	Nonlinear boundary value problems for ordinary differential equations
34B10	Nonlocal and multipoint boundary value problems for ordinary differential equations
47N20	Applications of operator theory to differential and integral equations

Keywords:

differential equation; fractional order; three-point boundary conditions; existence; fixed point