Correction to: Scientific Reports https://doi.org/10.1038/s41598-024-77715-w, published online 08 November 2024

The original version of this Article contained an error in Affiliation 9, which was incorrectly given as ‘Department of Mathematics, College of Education, ElFasher University, ElFasher, South Sudan’. The correct affiliation is listed below:

Department of Mathematics, College of Education, Elfasher University, El Fasher, Sudan

The original Article has been corrected.