Abstract
In this paper, we study the multi-point boundary value problems for a new kind of piecewise differential equations with left and right fractional derivatives and delay. In this system, the state variables satisfy the different equations in different time intervals, and they interact with each other through positive and negative delay. Some new results on the existence, no-existence and multiplicity for the positive solutions of the boundary value problems are obtained by using Guo–Krasnoselskii’s fixed point theorem and Leggett–Williams fixed point theorem. The results for existence highlight the influence of perturbation parameters. Finally, an example is given out to illustrate our main results.
Highlights
Fractional calculus has been widely used in various fields of science and technology, and the theoretical research of fractional differential equations has received extensive attention, see [5–8, 10, 12–15, 17, 18, 22, 23, 25, 27, 30–34, 36] and the references therein
The differential equation with left and right fractional derivatives have been studied extensively due to the wide application [2–4, 16, 24, 29]
In order to illustrate the applicability of our main results, the following boundary value problem is considered
Summary
Fractional calculus has been widely used in various fields of science and technology, and the theoretical research of fractional differential equations has received extensive attention, see [5–8, 10, 12–15, 17, 18, 22, 23, 25, 27, 30–34, 36] and the references therein. The differential equation with left and right fractional derivatives have been studied extensively due to the wide application [2–4, 16, 24, 29]. In [2], the following nonlocal boundary value problems of integro-differential equations involving mixed left and right fractional derivatives and left and right fractional integrals are studied cD1α− RLD0β+ y(t) + λI1p− I0q+ h t, y(t) = f t, y(t) , t ∈ J := [0, 1], y(0) = y(ξ) = 0, y(1) = δy(μ), 0 < ξ < μ < 1, where 1 < α 2, 0 < β 1 and p, q > 0, f, h : [0, 1] × R → R are given continuous functions, and δ, λ, μ ∈ R are constants. We discuss the multi-point boundary value problems for piecewise differential equations with left and right fractional derivatives and delay c t. An example is given out to illustrate our main results
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.
