The existence of solutions for boundary value problems of two types fractional perturbation differential equations

• Published in: Journal of applied mathematics & computing Vol. 48; no. 1-2; pp. 187 - 203
• Main Authors: Yan, Ri-An, Sun, Shu-Rong, Yang, Dian-Wu
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2015; Springer Nature B.V
• Subjects: Boundary value problems; Computational Mathematics and Numerical Analysis; Derivatives; Differential equations; Existence theorems; Investigations; Mathematical analysis; Mathematical and Computational Engineering; Mathematical functions; Mathematical models; Mathematics; Mathematics and Statistics; Mathematics of Computing; Original Research; Perturbation methods; Studies; Texts; Theorems; Theory of Computation; United States > US; Fractional boundary value problem; 35J05; Boundary value problem; Fixed point theorem; 34A08; 34B18
• ISSN: 1598-5865; 1865-2085
• DOI: 10.1007/s12190-014-0798-x

In this paper, we study the existence of solutions for the boundary value problems of fractional perturbation differential equations D α x ( t ) f ( t , x ( t ) ) = g ( t , x ( t ) ) , a . e . t ∈ J = [ 0 , 1 ] , or D α x ( t ) - f ( t , x ( t ) ) = g ( t , x ( t ) ) , a . e . t ∈ J , subject to x ( 0 ) = y ( x ) , x ( 1 ) = m , where 1 < α < 2 , D α is the standard Caputo fractional derivatives. Using some fixed point theorems, we prove the existence of solutions to the two types. For each type we give an example to illustrate our results.