About the Authors

Mukhtar M. Salah

Roles Data curation, Formal analysis, Methodology, Project administration

Affiliation Department of Mathematics, College of Science in Al-Zulfi, Majmaah University, Majmaah, Saudi Arabia

Essam A. Ahmed

Roles Conceptualization, Methodology, Software

essam.mohamed@science.sohag.edu.eg

Affiliation Mathematics Department, Sohag University, Sohag, Egypt

Ziyad A. Alhussain

Roles Writing – review & editing

Affiliation Department of Mathematics, College of Science in Al-Zulfi, Majmaah University, Majmaah, Saudi Arabia

Hanan Haj Ahmed

Roles Writing – review & editing

Affiliation Department of Basic Science, Preparatory Year Deanship, King Faisal University, Hofuf, Al-Ahsa, Saudi Arabia

M. El-Morshedy

Roles Data curation, Formal analysis

Affiliations Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, AlKharj, Saudi Arabia, Department of Mathematics, Faculty of Sciences, Mansoura University, Mansoura, Egypt

M. S. Eliwa

Roles Methodology, Software

Affiliations Department of Mathematics, College of Science in Al-Zulfi, Majmaah University, Majmaah, Saudi Arabia, Department of Mathematics, Faculty of Sciences, Mansoura University, Mansoura, Egypt

Competing Interests

The authors have declared that no competing interests exist.