About the Authors

Tabasam Rashid

Contributed equally to this work with: Tabasam Rashid, Asif Ali, Yu-Ming Chu

Roles Methodology, Supervision, Validation

Affiliation Department of Mathematics, School of Sciences, University of Management and Technology, Lahore, Pakistan

Asif Ali

Contributed equally to this work with: Tabasam Rashid, Asif Ali, Yu-Ming Chu

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

Affiliation Department of Mathematics, School of Sciences, University of Management and Technology, Lahore, Pakistan

Yu-Ming Chu

Contributed equally to this work with: Tabasam Rashid, Asif Ali, Yu-Ming Chu

Roles Funding acquisition, Project administration

chuyuming2005@126.com

Current address: Department of Mathematics, Huzhou University, Huzhou, P. R. China

Affiliation Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science Technology, Changsha, P.R. China

Competing Interests

The authors have declared that no competing interests exist.