About the Authors

Tasawar Hayat

Affiliations Department of Mathematics, Quaid-I-Azam University, 45320, Islamabad, 44000, Pakistan, Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, King Abdulaziz University, P. O. Box 80203, Jeddah, 21589, Saudi Arabia

Taseer Muhammad

taseer_muhammad@yahoo.com

Affiliation Department of Mathematics, Quaid-I-Azam University, 45320, Islamabad, 44000, Pakistan

Sabir Ali Shehzad

Affiliation Department of Mathematics, Comsats Institute of Information Technology, Sahiwal, 57000, Pakistan

Ahmed Alsaedi

Affiliation Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, King Abdulaziz University, P. O. Box 80203, Jeddah, 21589, Saudi Arabia

Competing Interests

The authors have declared that no competing interests exist.

Author Contributions

Conceived and designed the experiments: TH TM SAS AA. Performed the experiments: TH TM SAS AA. Analyzed the data: TH TM SAS AA. Contributed reagents/materials/analysis tools: TH TM SAS AA. Wrote the paper: TH TM SAS AA.