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, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

Sumaira Qayyum

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

Maria Imtiaz

mi_qau@gmail.com

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

Ahmed Alsaedi

Affiliation Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

Competing Interests

The authors have declared that no competing interests exist.

Author Contributions

Conceived and designed the experiments: TH SQ MI AA. Performed the experiments: TH SQ MI AA. Contributed reagents/materials/analysis tools: TH SQ MI AA. Wrote the paper: TH SQ MI AA.