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, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia

Taseer Muhammad

taseer_qau@yahoo.com

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

Ahmed Alsaedi

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

Meraj Mustafa

Affiliation School of Natural Sciences (SNS), National University of Sciences and Technology (NUST), Islamabad 44000, Pakistan

Competing Interests

The authors have declared that no competing interests exist.

Author Contributions

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