Nyamoradi, NematZhou, YongAhmad, BashirAlsaedi, Ahmed2022-01-052022-01-052018-01-24Nyamoradi, 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. 1-13.1072-6691https://hdl.handle.net/10877/15090In 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+).Text13 pages1 file (.pdf)enAttribution 4.0 InternationalTempered fractional calculusKirchhoff type problemsVariational methodsArticle