id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
cana-510	B.D. Karande	Some Applications of Fractional Derivative Operator	2024	12	.pdf	application/pdf	3562	229	86	Now, 𝑢 ∈ 𝑇𝑆(𝜔, 𝜎, ς, 𝜗), since ∑ [𝜔(𝑛 − 1) + ς(𝑛𝜎 + 1 − 𝜔)]𝛩(𝑛, 𝜗) ς(𝜎 + (1 − 𝜔)) ∞ 𝑛=2 × ς(𝜎 + (1 − 𝜔))𝜃𝑛 [𝜔(𝑛 − 1) + ς(𝑛𝜎 + 1 − 𝜔)]𝛩(𝑛, 𝜗) = ∑ 𝜃𝑛 ∞ 𝑛=2 = 1 − 𝜃1 ≤ 1. Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 31 No. 2 (2024) 30 https://internationalpubls.com Conversely, suppose 𝑢 ∈ 𝑇𝑆(𝜔, 𝜎, ς, 𝜗). [𝜔(𝑛 − 1) + ς(𝑛𝜎 + 1 − 𝜔)]2𝛩(𝑛, 𝜗) − ς2(𝜎 + (1 − 𝜔))(𝑛𝜎 + 1 − 𝜔) .	cache/cana-510.pdf	txt/cana-510.txt