Araz, Seda Igret2024-12-242024-12-2420211937-16321937-1179https://doi.org/10.3934/dcdss.2021053https://hdl.handle.net/20.500.12604/8364In this paper, we introduce a new fractional integro-differential equation involving newly introduced differential and integral operators socalled fractal-fractional derivatives and integrals. We present a numerical scheme that is convenient for obtaining solution of such equations. We give the general conditions for the existence and uniqueness of the solution of the considered equation using Banach fixed-point theorem. Both the suggested new equation and new numerical scheme will considerably contribute for our readers in theory and applications.eninfo:eu-repo/semantics/openAccessKey words and phrasesFractal-fractional derivativeFractal-fractional integralfractional integro-differential equationnew numerical schemeArticle14722972309Q2WOS:000661878900018Q12-s2.0-8510916956310.3934/dcdss.2021053