About the Authors

Shahzaib Ashraf

Roles Conceptualization, Methodology, Supervision, Writing – review & editing

Affiliation Institute of Mathematics, Khwaja Fareed University of Engineering & Information Technology, Rahim Yar Khan, Pakistan

Muhammad Sohail

Roles Conceptualization, Project administration, Software, Writing – review & editing

muhammad_sohail111@yahoo.com (MS); sayed.eldin22@fue.edu.eg (SME)

Affiliation Institute of Mathematics, Khwaja Fareed University of Engineering & Information Technology, Rahim Yar Khan, Pakistan

Adan Fatima

Roles Conceptualization, Methodology, Software, Writing – original draft

Affiliation Institute of Mathematics, Khwaja Fareed University of Engineering & Information Technology, Rahim Yar Khan, Pakistan

Sayed M. Eldin

Roles Funding acquisition, Software, Validation, Writing – review & editing

muhammad_sohail111@yahoo.com (MS); sayed.eldin22@fue.edu.eg (SME)

Affiliation 2 Center of Research, Faculty of Engineering, Future University in Egypt, New Cario, Egypt

Competing Interests

The authors have declared that no competing interests exist.