Positive solutions for boundary value problem of nonlinear fractional functional differential equations

• Published in: Applied mathematics and computation Vol. 217; no. 22; pp. 9278 - 9285
• Main Authors: Li, Xiaoyan, Liu, Song, Jiang, Wei
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Inc 15.07.2011; Elsevier
• Subjects: Boundaries; Boundary value problem; Captuo derivative; Derivatives; Difference and functional equations, recurrence relations; Differential equations; Exact sciences and technology; Existence theorems; Finite differences and functional equations; fractional functional differential equation; Mathematical analysis; Mathematical models; Mathematics; Nonlinearity; Numerical analysis; Numerical analysis. Scientific computation; Ordinary differential equations; Partial differential equations, boundary value problems; Positive solution; Sciences and techniques of general use; fractional functional differential equation; Boundary value problem; Positive solution; Captuo derivative; Transcendental equation; Existence condition; Differential equation; Existence of solution; Recurrence relation; Functional equation; Boundary condition; Difference equation; Partial differential equation; Non linear equation; Numerical analysis; Fixed point theorem; Applied mathematics; Captuo derivative fractional functional differential equation
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2011.04.006

In this paper, we investigate the existence of positive solutions for the nonlinear Captuo fractional order functional differential equation D 0 + α u ( t ) + a ( t ) f ( u t ) = 0 , 0 < t < 1 , 1 < α ⩽ 2 , where D 0 + α is the Captuo fractional order derivative, subject to the boundary conditions - au ( t ) + bu ′ ( t ) = ξ ( t ) , - τ ⩽ t ⩽ 0 , cu ( t ) + du ′ ( t ) = η ( t ) , 1 ⩽ t ⩽ 1 + β , we obtain the existence results of positive solutions by using some fixed point theorems.