id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-6462	Anakira, Nidal ; Amourah, Ala ; Almalki, Adel ; Alsoboh, Abdullah ; Sasa, Tala	Exact Solutions of Nonlinear Delay Voltera Integro-Differential Equations Using Modified Homotopy Perturbation Method	2025	16	.pdf	application/pdf	5342	347	59	− F (r) is named deformation, Furthermore, L(u) − L (v0) and N. Anakira et al. / Eur. = −x2 8 − 5x3 64 + 5x4 768 + 19x5 12288 − 7x6 184320 − 383x7 41287680 + 5x8 33030144 + 307x9 9512681472 − 97x10 237817036800 − 6143x11 83711596953600 + x12 502269581721600 , (31) u′3(x) = − x3 192 − 47x4 12288 + 329x5 122880 − 941x6 4718592 − 22217x7 165150720 + 471809x8 84557168640 + 1963291x9 761014517760 − 22998401x10 487049291366400 − 47100961x11 1785847401676800 + 37961641x12 164583696538533888 + 9442463747x13 53489701375023513600 − 25965661x14 34038900875014963200 − 1419107x15 1687625794584576000 + 24349x16 18001341808902144000 + 639917x17 229517108063502336000 − 17x18 11572291162865664000 − 2085431x19 337725745297071538176000 + 51622011x21 51843864409638174720000 + x22 209034461299661120471040000 − 1 2281130034024079687680000 + x23 161175523684005374412718080000 , (32) Up to the n′th order problem, and by solving these problems and substituting them in (??) , we have the HPM approximate solutions of order five ũ(x) = 1− x2 2 + x4 24 − x6 720 + x7 5284823040 + 133153x8	cache/ejpam-6462.pdf	txt/ejpam-6462.txt