Atangana, AbdonAraz, Seda Igret2024-12-242024-12-2420190960-07791873-2887https://doi.org/10.1016/j.chaos.2019.06.005https://hdl.handle.net/20.500.12604/6401We have introduced a new partial integro-differential equation with mixed fractional operators. The differential operator can be taken as Caputo while the integral is consider to be Caputo-Fabrizio or the Atangana-Baleanu integral. We presented the well poseness of the new class of partial differential equation. We presented the conditions which the existence and uniqueness are obtained. We presented the derivation of exact solution under some conditions. We suggested a numerical scheme that will be used to solve such mathematical equations. We presented some illustratives examples. (C) 2019 Elsevier Ltd. All rights reserved.eninfo:eu-repo/semantics/closedAccessFractional differentiationFractional integrationNew numerical schemesNew partial differential equationArticle127257271Q1WOS:000487764300024Q12-s2.0-8506849789410.1016/j.chaos.2019.06.005