id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
american_scientific_journal-3270	Khayyat, Hassan	On Treating of Surface Cracks in Finite Layers of Fractional Materials	2017	18	.pdf	application/pdf	6785	454	82	The tractions ( , ), ( 1,2)iP x t i = , have the following properties [ ]1 1 2 2( , ) ( , ), ( , ) ( , ), | | 1, 0, ; 1.P x t P x t P x t P x t x t T T= − = − − < ∈ < . (2.24) Using above information and the following symmetric properties in the presence of time 1 1 2 2( , ) ( , ); ( , ) ( , )f x t f x t f x t f x t= − = − − , we get 1 1 3 11 12 1 1 20 3 1 0 1 1 ( , ) lim ( , ) cos ( ) ( , )y y K a aP x t f z t dz e z x d f z t dzα α α µ π π− ∞ → − − + − = − + ×  ∫ ∫ ∫ 1 2 1 1 10 1 0 1sin ( ) ( , ) ( , ) ( ) ( ,	cache/american_scientific_journal-3270.pdf	txt/american_scientific_journal-3270.txt