id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
iajs-2485	Kadhem, Hasan Shather; Hasan, Sameer Qasim	Solving Some Fractional Partial Differential Equations by Invariant Subspace and Double Sumudu Transform Methods	2020	13	.pdf	application/pdf	3778	188	72	𝑡 𝐸 𝑥 𝐵𝐸 𝑡 𝐸 𝑥 From our conditions, we have 𝑓 𝑥, 0 𝐸 𝑥 1 2 𝐸 𝑥 𝐸 𝑥 𝐴𝐸 𝑥 𝐵𝐸 𝑥 Thus, 𝐴 𝐵 and 𝑓 𝑥, 𝑡 𝐸 𝑡 𝐸 𝑥 𝐸 𝑡 𝐸 𝑥 For 𝛼 𝛽 1 𝑓 𝑥, 𝑡 1 2 𝑒 𝑒 cosh 𝑥 𝑡 which agree with that in double Sumudu transform method. If the double Sumudu transform of the function f (x; t) given by 𝑆 𝑓 𝑥, 𝑡 𝑇 𝑢, 𝑣 , then: 1. 𝑆 𝑥 𝑓 𝑥, 𝑡 𝑢 ∑ 𝑎 𝑢 𝑇 𝑢, 𝑣 2. 𝑆 𝑥 𝑡 𝑓 𝑥, 𝑡 𝑢 𝑣 ∑ 𝑎 𝑏 𝑢 𝑣 𝑇 𝑢, 𝑣 where 𝑎 1, 𝑎 1, 𝑎 𝑛! 𝑛, 𝑎 𝑎 𝑚 𝑘 𝑎 , similarly for 𝑏 The double Sumudu transform of the partial Caputo fractional derivatives are given in the following theorem :	cache/iajs-2485.pdf	txt/iajs-2485.txt