About the Authors

Muhammad Farhan

Roles Data curation, Formal analysis, Investigation, Methodology, Writing – original draft

Affiliations School of Mathematical Science, Yangzhou University, Yangzhou, China, Department of Mathematics, Abdul Wali Khan University Mardan, Mardan, Khyber Pakhtunkhwa, Pakistan

Zahir Shah

Roles Conceptualization, Data curation, Formal analysis, Investigation, Supervision, Validation

zahir1987@yahoo.com

Affiliation Department of Mathematical Sciences, University of Lakki Marwat, Lakki Marwat, KPK, Pakistan

Zhi Ling

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

Affiliation School of Mathematical Science, Yangzhou University, Yangzhou, China

Kamal Shah

Roles Formal analysis, Methodology, Software, Validation, Writing – original draft

Affiliations Department of Mathematics and Sciences, Prince Sultan University, Riyadh, Saudi Arabia, Department of Computer Science and Mathematics Lebanese American University, Byblos, Lebanon

Thabet Abdeljawad

Roles Funding acquisition, Project administration, Software, Supervision, Visualization

Affiliation Department of Mathematics and Sciences, Prince Sultan University, Riyadh, Saudi Arabia

Saeed Islam

Roles Formal analysis, Investigation, Resources, Software, Supervision, Validation, Visualization

Affiliation Department of Mathematics, Abdul Wali Khan University Mardan, Mardan, Khyber Pakhtunkhwa, Pakistan

Hakim A. L. Garalleh

Roles Funding acquisition, Methodology, Software, Writing – original draft

Affiliation Department of Mathematical Science, College of Engineering, University of Business and Technology, Jeddah, Saudi Arabia

Competing Interests

The authors have declared that no competing interests exist.