id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-5592	Hammad, Hasanen A.; De la Sen, Manuel 	Gronwall-Type Inequalities and Qualitative Studies onHigher-Variable Orders of Atangana-Baleanu Fractional Operators via Increasing Functions	2024	21	.pdf	application/pdf	6697	423	81	κ ψ′(r)Lθu ( −θu 1− θu (ψ(z)− ψ(r))θu ) ℘ (k+1) ψ (r) dr = Λ(ϖu − k) (k + 1−ϖu) × z∫ κ ψ′(r)Lϖu−k ( − (ϖu − k) k + 1−ϖu (ψ(z)− ψ(r))ϖu−k ) ℘ (k+1) ψ (r) dr, where ℘ (k) ψ (z) = ( 1 ψ′(z) = k + 1−ϖu Λ(ϖu − k) RL ℜk,ψκ ℘ (z) + ϖu − k Λ(ϖu − k) RL ℜϖu,ψκ ℘ (z) , where ℜk,ψκ takes the form ℜk,ψκ ℘ (z) = 1 Γ (k) z∫ κ ψ′(r)	cache/ejpam-5592.pdf	txt/ejpam-5592.txt