Tyagi, J.J.Tyagi2025-08-312025-08-312021-06-0110.1007/s13324-021-00494-42-s2.0-85101150729https://d8.irins.org/handle/IITG2025/25406We establish a generalization of Sturm–Picone comparison theorem for a pair of fractional nonlocal equations: (-div.(A1(x)∇))su=C1(x)uinΩ,u=0on∂Ω,and (-div.(A2(x)∇))sv=C2(x)vinΩ,v=0on∂Ω,where Ω ⊂ Rⁿ is an open bounded subset with smooth boundary, 0<s<1,A1,A2 are smooth, real symmetric and positive definite matrices on Ω ¯ and C<inf>1</inf>, C<inf>2</inf>∈ C^α(Ω ¯).falseFractional Laplacian | Leighton’s variational lemma | Sturm–Picone comparison theorem | Variational methodsArticle1664235XJune 2021061arJournal0