About the Authors
- Muhammad Farhan
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Roles Data curation, Formal analysis, Investigation, Methodology, Writing – original draft
Affiliations School of Mathematical Science, Yangzhou University, Yangzhou, China, Department of Mathematics, Abdul Wali Khan University Mardan, Mardan, Khyber Pakhtunkhwa, Pakistan
- Zahir Shah
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Roles Conceptualization, Data curation, Formal analysis, Investigation, Supervision, Validation
* E-mail: zahir1987@yahoo.com
Affiliation Department of Mathematical Sciences, University of Lakki Marwat, Lakki Marwat, KPK, Pakistan
- Zhi Ling
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Roles Funding acquisition, Investigation, Software, Supervision, Validation, Writing – review & editing
Affiliation School of Mathematical Science, Yangzhou University, Yangzhou, China
- Kamal Shah
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Roles Formal analysis, Methodology, Software, Validation, Writing – original draft
Affiliations Department of Mathematics and Sciences, Prince Sultan University, Riyadh, Saudi Arabia, Department of Computer Science and Mathematics Lebanese American University, Byblos, Lebanon
- Thabet Abdeljawad
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Roles Funding acquisition, Project administration, Software, Supervision, Visualization
Affiliation Department of Mathematics and Sciences, Prince Sultan University, Riyadh, Saudi Arabia
- Saeed Islam
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Roles Formal analysis, Investigation, Resources, Software, Supervision, Validation, Visualization
Affiliation Department of Mathematics, Abdul Wali Khan University Mardan, Mardan, Khyber Pakhtunkhwa, Pakistan
- Hakim A. L. Garalleh
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Roles Funding acquisition, Methodology, Software, Writing – original draft
Affiliation Department of Mathematical Science, College of Engineering, University of Business and Technology, Jeddah, Saudi Arabia
Competing Interests
The authors have declared that no competing interests exist.