About the Authors

Ahmed Younes

ayounes2@yahoo.com

Affiliation Department of Mathematics and Computer Science, Faculty of Science, Alexandria University, Alexandria, Egypt

Mahmoud Abdel-Aty

Affiliations University of Science and Technology, Zewail City of Science and Technology, Cairo, Egypt, Department of Mathematics, Faculty of Science, Sohag University, Sohag, Egypt

Competing Interests

The authors have declared that no competing interests exist.

Author Contributions

Conceived and designed the experiments: AY. Performed the experiments: AY. Analyzed the data: AY MA. Contributed reagents/materials/analysis tools: AY MA. Contributed to the writing of the manuscript: AY MA.