id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
cana-4138	Kamble Rajratna M	Existence and Uniqueness of Continuous Solutions for Conformable Fractional Integro-Differential Equations in Cone Metric Spaces	2025	9	.pdf	application/pdf	3689	213	72	𝐼 × 𝐼 → ℝ+ and a comparison function 𝜙: ℝ2 → ℝ2 satisfying (‖𝑘(𝑡, 𝑠, 𝑢) − 𝑘(𝑡, 𝑠, 𝑣)‖, 𝑎‖𝑘(𝑡, 𝑠, 𝑢) − 𝑘(𝑡, 𝑠, 𝑣)‖) ≤ 𝑝1(𝑡, 𝑠)𝜙(𝑑(𝑢, 𝑣)) (‖ℎ(𝑡, 𝑠, 𝑢) − ℎ(𝑡, 𝑠, 𝑣)‖, 𝑎‖ℎ(𝑡, 𝑠, 𝑢) − ℎ(𝑡, 𝑠, 𝑣)‖) ≤ 𝑝2(𝑡, 𝑠)𝜙(𝑑(𝑢, 𝑣)) where the metric 𝑑: 𝐵 × 𝐵 ⟶ ℝ is defined by 𝑑(𝑥, 𝑦) − 𝑘(𝑡, 𝑠, 𝑦(𝑠))|) = (|𝑡2𝑠2 + 𝑥𝑠2 2 − 𝑡2𝑠2 − 𝑦𝑠2 2 | , 𝑎 |𝑡2𝑠2 + 𝑥𝑠2 2 − 𝑡2𝑠2 − 𝑦𝑠2 2 |) = (| 𝑥𝑠2 2 − 𝑦𝑠2 2 | , 𝑎 | 𝑥𝑠2 2 − 𝑦𝑠2 2 |) = 𝑠2 2 (|𝑥 − 𝑦|, 𝑎|𝑥 − 𝑦|) ≤ 𝑠2 2 (‖𝑥 − 𝑦‖∞, 𝑎‖𝑥 − 𝑦‖∞) = 𝑝1 ∗𝜙∗(‖𝑥 − 𝑦‖∞, 𝑎‖𝑥 − 𝑦‖∞) where 𝑝1 ∗ = 𝑠2, which is a continuous function from [0,1] ×	cache/cana-4138.pdf	txt/cana-4138.txt