About the Authors

Mian Imad Shah

Roles Conceptualization, Formal analysis

Affiliation Department of Mathematics and Statistics, University of Swat, Khyber Pakhtunkhwa, Pakistan

Eltigani Ismail Hassan

Roles Investigation, Supervision

Affiliation Department of Mathematics and Statistics, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, Saudi Arabia

Amjad Ali

Roles Methodology, Software, Writing – original draft

Affiliation Department of Mathematics and Statistics, University of Swat, Khyber Pakhtunkhwa, Pakistan

Abdulghani Muhyi

Roles Investigation, Validation, Writing – review & editing

muhyi2007@gmail.com (AM); aldwoah@iu.edu.sa (KA)

Affiliations Department of Mathematics, Hajjah University, Hajjah, Yemen, Department of Mechatronics Engineering, Faculty of Engineering and Smart Computing, Modern Specialized University, Sana’a, Yemen

Waleed Eltayeb Ahmed

Roles Investigation, Resources

Affiliation Department of Mathematics and Statistics, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, Saudi Arabia

Khaled Aldwoah

Roles Conceptualization, Project administration, Validation, Writing – review & editing

muhyi2007@gmail.com (AM); aldwoah@iu.edu.sa (KA)

Affiliation Department of Mathematics, Faculty of Science, Islamic University of Madinah, Madinah, Saudi Arabia

Competing Interests

The authors have declared that no competing interests exist.