Fractional Sobolev’s Spaces on Time Scales via Conformable Fractional Calculus and Their Application to a Fractional Differential Equation on Time Scales
Joint Authors
Wang, Yanning
Zhou, Jianwen
Li, Yongkun
Source
Advances in Mathematical Physics
Issue
Vol. 2016, Issue 2016 (31 Dec. 2016), pp.1-21, 21 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2016-11-23
Country of Publication
Egypt
No. of Pages
21
Main Subjects
Abstract EN
Using conformable fractional calculus on time scales, we first introduce fractional Sobolev spaces on time scales, characterize them, and define weak conformable fractional derivatives.
Second, we prove the equivalence of some norms in the introduced spaces and derive their completeness, reflexivity, uniform convexity, and compactness of some imbeddings, which can be regarded as a novelty item.
Then, as an application, we present a recent approach via variational methods and critical point theory to obtain the existence of solutions for a p-Laplacian conformable fractional differential equation boundary value problem on time scale T: Tα(Tαup-2Tα(u))(t)=∇F(σ(t),u(σ(t))), Δ-a.e.
t∈a,bTκ2, u(a)-u(b)=0, Tα(u)(a)-Tα(u)(b)=0, where Tα(u)(t) denotes the conformable fractional derivative of u of order α at t, σ is the forward jump operator, a,b∈T, 01, and F:[0,T]T×RN→R.
By establishing a proper variational setting, we obtain three existence results.
Finally, we present two examples to illustrate the feasibility and effectiveness of the existence results.
American Psychological Association (APA)
Wang, Yanning& Zhou, Jianwen& Li, Yongkun. 2016. Fractional Sobolev’s Spaces on Time Scales via Conformable Fractional Calculus and Their Application to a Fractional Differential Equation on Time Scales. Advances in Mathematical Physics،Vol. 2016, no. 2016, pp.1-21.
https://search.emarefa.net/detail/BIM-1095957
Modern Language Association (MLA)
Wang, Yanning…[et al.]. Fractional Sobolev’s Spaces on Time Scales via Conformable Fractional Calculus and Their Application to a Fractional Differential Equation on Time Scales. Advances in Mathematical Physics No. 2016 (2016), pp.1-21.
https://search.emarefa.net/detail/BIM-1095957
American Medical Association (AMA)
Wang, Yanning& Zhou, Jianwen& Li, Yongkun. Fractional Sobolev’s Spaces on Time Scales via Conformable Fractional Calculus and Their Application to a Fractional Differential Equation on Time Scales. Advances in Mathematical Physics. 2016. Vol. 2016, no. 2016, pp.1-21.
https://search.emarefa.net/detail/BIM-1095957
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1095957