Abstract
In this paper, a functional boundary value problem of fractional differential equations is studied. Based on Mawhin’s coincidence degree theory, some existence theorems are obtained in the case of nonresonance and the cases of and at resonance.
Highlights
The subject of fractional calculus has gained considerable popularity and importance because of its frequent appearance in various fields such as physics, chemistry, and engineering
There have been some papers dealing with the basic theory for initial value problems of nonlinear fractional differential equations; for example, see [, ]
There are some articles which deal with the existence and multiplicity of solutions for nonlinear boundary value problems of fractional order differential equations using techniques of topological degree theory
Summary
The subject of fractional calculus has gained considerable popularity and importance because of its frequent appearance in various fields such as physics, chemistry, and engineering. There are some articles which deal with the existence and multiplicity of solutions for nonlinear boundary value problems of fractional order differential equations using techniques of topological degree theory. Jiang [ ] studied the existence of a solution for the following fractional differential equation at resonance under the case dim Ker L = : Dα +u(t) = f t, u(t), Dα +– u(t) , u( ) = , m. Being directly inspired by [ , , ], we intend in this paper to study the following functional boundary value problems (FBVP) of fractional order differential equation: Dα +u(t) = f t, u(t), Dα +– u(t), Dα +– u(t) ,. To the best of our knowledge, the method of Mawhin’s theorem has not been developed for fractional order differential equation with functional boundary value problems at resonance.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
