Nonlocal boundary value problems of fractional order at resonance with integral conditions

作者：Zhang, Hai-E^*

来源：Advances in Difference Equations, 2017, 2017(1): 326.

DOI：10.1186/s13662-017-1379-8

• fractional differential equation
• resonance
• Riemann-Stieltjes integral
• coincidence degree theory

Based upon the well-known coincidence degree theory of Mawhin, we obtain some new existence results for a class of nonlocal fractional boundary value problems at resonance given by @@@ {D(0+)(alpha)u(t) = f (t, u(t), D(0+)(alpha-1)u(t), D(0+)(alpha-2)u(t)), t is an element of (0, 1), @@@ (beta-alpha)(0+)u(0) = u'(0) = 0, D(0+)(beta)u(1) = integral(1)(0) D(0+)(beta)u(t) dA(t), @@@ where alpha, beta are real numbers with 2 < alpha <= 3, 0 < beta <= 1, D-0+(alpha) and I-0+(alpha) respectively denote Riemann-Liouville derivative and integral of order alpha, f : [0, 1] x R-3 -> R satisfies the Caratheodory conditions, integral(1)(0) D(0+)(beta)u(t) dA(t) is a Riemann-Stieltjes integral with integral(1)(0)t(alpha-beta-1) dA(t) = 1. We also present an example to demonstrate the application of the main results.

• 出版日期2017-10-13
• 单位唐山学院