0577699 20240402214700.120231107235959.9 85162955071 001013279000001 10.1002/mma.9486 10 s. P cav_un_epca*02572240170-42144616 (2023)17010-17019Wiley Babenko's approach Banach's contractive principle multivariate Mittag–Leffler function nonlinearpartial integro-differential equation cav_un_auth*0455888 Li Ch. CA cav_un_auth*0457625 Saadaty R. IR 20 K cav_un_auth*0457626 O'Regan D. IE 20 cav_un_auth*0101163 Mesiar Radko UTIA-B Ekonometrie Department of Econometrics E E Department of Econometrics 20 Ústav teorie informace a automatizace AV ČR, v. v. i. cav_un_auth*0457627 Hrytsenko A. CA 20 http://library.utia.cas.cz/separaty/2023/E/mesiar-0577699.pdf https://onlinelibrary.wiley.com/doi/10.1002/mma.9486 In this work, we study a new nonlinear partial integro-differential equation withnonlocal initial value conditions and investigate the solutions of this equation.By considering an equivalent implicit integral equation via series, we provethe uniqueness of solutions of the equation by Babenko's approach, Banach'scontraction principle, and the multivariable Mittag–Leffler function. We alsodemonstrate the application of our key theorem with an illustrative example. WOS BA 10000 10100 10101 2024 5 RVO:67985556 https://hdl.handle.net/11104/0347643 S Article Mathematics Applied A MATHEMATICS.APPLIED 2 0.6 3.7 0.01603 0.47 12357 87 0.607 35.27 2.33 5866 Q2 1.900 838 Q1 84.2 Q3 Q2 1.38 Q1 84.2 2023 85162955071 SCOPUS PUBMED 001013279000001 WOS cav_un_epca*0257224 Mathematical Methods in the Applied Sciences Roč. 46 č. 16 2023 17010 17019 0170-4214 1099-1476 Wiley