Abstract
AbstractIn this paper, we consider a Riemann–Liouville type two-term fractional differential equation boundary value problem. Some positive properties of the Green’s function are deduced by using techniques of analysis. As application, we obtain the existence and multiplicity of positive solutions for a fractional boundary value problem under conditions that the nonlinearity $f(t,x)$f(t,x) may change sign and may be singular at $t = 0,1$t=0,1 and $x=0$x=0, and we also obtain the uniqueness results of positive solution for a singular problem by means of the monotone iterative technique.
Funder
Natural Science Foundation of Shandong Province of China
National Natural Science Foundation of China
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Algebra and Number Theory,Analysis
Reference34 articles.
1. Bagley, R., Torvik, P.: On the appearance of the fractional derivative in the behaviour of real materials. J. Appl. Mech. 51, 294–298 (1984)
2. Metzler, R., Klafter, J.: Boundary value problems for fractional diffusion equations. Physica A 278, 107–125 (2000)
3. Diethelm, K., Luchko, Y.: Numerical solution of linear multi-term initial value problems of fractional order. J. Comput. Anal. Appl. 6, 243–263 (2004)
4. Ford, N., Connolly, J.: Systems-based decomposition schemes for the approximate solution of multi-term fractional differential equations. Comput. Appl. Math. 229, 382–391 (2009)
5. Elshehawey, E., Elbarbary, E., Afifi, N., El-Shahed, M.: On the solution of the endolymph equation using fractional calculus. Appl. Math. Comput. 124, 337–341 (2001)
Cited by
14 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献