Variational methods for Kirchhoff type problems with tempered fractional derivative

Date
2018-01-24
Authors
Nyamoradi, Nemat
Zhou, Yong
Ahmad, Bashir
Alsaedi, Ahmed
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
In this article, using variational methods, we study the existence of solutions for the Kirchhoff-type problem involving tempered fractional derivatives M(∫ℝ |Dα,λ+ u(t)|2dt) Dα,λ_ (Dα,λ+ u(t)) = ƒ(t, u(t)), t ∈ ℝ, u ∈ Wα,2λ(ℝ), where Dα,λ± u(t) are the left and right tempered fractional derivatives of order α ∈ (1/2, 1], λ > 0, Wα,2λ(ℝ) represent the fractional Sobolev space, ƒ ∈ C(ℝ x ℝ, ℝ) and M ∈ C(ℝ+, ℝ+).
Description
Keywords
Tempered fractional calculus, Kirchhoff type problems, Variational methods
Citation
Nyamoradi, N., Zhou, Y., Ahmad, B., & Alsaedi, A. (2018). Variational methods for Kirchhoff type problems with tempered fractional derivative. <i>Electronic Journal of Differential Equations, 2018</i>(34), pp. 1-13.