id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-6481	Shah, Sajid Ali; Rehman, Nasir; Ahmad, Sadique ; A.Elaffendi, Mohammed ; Ateya, Abdelhamied Ashraf 	Fractional Discrete Modeling and Numerical Analysis of Hepatitis B and C Dynamics with Neural Network Approximation	2025	19	.pdf	application/pdf	6928	378	73	For t ∈ [ξ − 1, b+ ξ]Nξ−1 , one has |g(t)− ḡ(t)| = ∣∣∣g(t)− ( g(0) + 1 Γ(ξ) t−ξ∑ s=0 (t− s− 1)ξ−1F (s + ξ − 1, g(s + ξ − 1)) )∣∣∣, ≤ Dψϵ+ 1 Γ(ξ) t−ξ∑ s=0 (t− s− 1)ξ−1 × |F (s + ξ − 1, g(s + ξ − 1))− F (s + ξ − 1, ḡ(s + ξ − 1))|, ≤ Dψϵ+ 1 Γ(ξ) t−ξ∑ s=0 (t− s− 1)ξ−1K∥g − ḡ∥ (18) which further means ∥g − ḡ∥ ≤ [ Dψ 1−KDψ ] ϵ = Dgϵ. (19) Also set Dg = Dψ 1−KDψ > 0, we conclude that solution of (2) is UH stable. = ηH(t+ ξ − 1)V (t+ ξ − 1)− γI(t+ ξ − 1), C∆ξR(t)	cache/ejpam-6481.pdf	txt/ejpam-6481.txt