Details

Autor(en) / Beteiligte

• Jiao, Feng
• Zhou, Yong

Titel

Existence of solutions for a class of fractional boundary value problems via critical point theory

Ist Teil von

• Computers & mathematics with applications (1987), 2011-08, Vol.62 (3), p.1181-1199

Ort / Verlag

Elsevier Ltd

Erscheinungsjahr

2011

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• In this paper, by the critical point theory, a new approach is provided to study the existence of solutions to the following fractional boundary value problem: { d d t ( 1 2 0 D t − β ( u ′ ( t ) ) + 1 2 t D T − β ( u ′ ( t ) ) ) + ∇ F ( t , u ( t ) ) = 0 , a.e.  t ∈ [ 0 , T ] , u ( 0 ) = u ( T ) = 0 , where 0 D t − β and t D T − β are the left and right Riemann–Liouville fractional integrals of order 0 ≤ β < 1 respectively, F : [ 0 , T ] × R N → R is a given function and ∇ F ( t , x ) is the gradient of F at x . Our interest in this problem arises from the fractional advection–dispersion equation (see Section  2). The variational structure is established and various criteria on the existence of solutions are obtained.