College of Sciences, University of Shanghai for Science and Technology, Shanghai 200093, China
In this paper, we study the existence of positive solutions for a class of fractional functional integro-differential equations with two fractional derivative terms. First, we transform the boundary value problem into an equivalent integral equation, establish the operator T and prove its full continuity, then the existence theorems of positive solutions of boundary value problems is established by using the fixed point theorems of cone extension and cone compression.
Caputo fractional derivatives, functional integro-differential equations, fixed point theorem, positive solutions
Xiaoying Yang. Existence of positive solutions for boundary value problems of nonlinear fractional functional integro-differential equations. Academic Journal of Mathematical Sciences (2021) Vol. 2, Issue 1: 1-6. https://doi.org/10.25236/AJMS.2021.020101.
 Bai, Z. (2012) The theory and application for boundary value problems of fractional differential equations. Bei Jing: China Science and Technology Press.
 Song, L. (2014) Existence of positive solutions for boundary value problems of fractional functional differential equations. Journal of Southwest Normal University (Natural Science Edition), 7, 1-7.
 Nouri, K., Nazari, M., Torkzadeh, L. (2018) Existence results of solutions for some fractional neutral functional integro-differential equations with infinite delay. Pushpa Publishing House, Allahabad, India, 19, 49-67.