Variational methods for Kirchhoff type problems with tempered fractional derivative
Texas State University, Department of Mathematics
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+).
Tempered fractional calculus, Kirchhoff type problems, Variational methods
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.