On positive solutions of fractional differential equations with change of sign. (28th March 2019)

• Record Type: Journal Article
• Authors: Wang, Fanglei; Zhang, Li; Ru, Yuanfang; Liu, Ronghua
• Is Part Of: Mathematical methods in the applied sciences. Volume 42:Number 11(2019)
• Page Start: 3900
• Page End: 3911
• Publication Date: 2019-03-28
• Subjects: Caputo's fractional derivative -- cone -- positive solution -- uniqueness; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.5619
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : We study the existence and uniqueness of positive solutions of fractional differential equations with change of sign D 0 + α ( u ′ ′ ( t ) ) = h ( t ) f ( u ( t ) ), 0 < t < 1, u ( 0 ) = u ( 1 ) = 0, u ′ ′ ( 0 ) = u ′ ′ ( 1 ) = 0, where 1 < α ≤ 2, h : [ 0, 1 ] → R is continuous and does not vanish identically on any subinterval of [0, 1].