1. Engineering Mathematics Department, Faculty of Engineering, Zagazig University, Zagazig, Egypt
2. Mechanical Engineering Department, Faculty of Engineering, Jazan University, Jazan, Kingdom of Saudi Arabia
3. Mechanical Design and Production Department, Faculty of Engineering, Zagazig University, Zagazig, Egypt
4. Mechanical Engineering Department, Faculty of Engineering, King Abdulaziz University, Jeddah, Saudi Arabia
5. Mathematical Department, Faculty of Science, Zagazig University, Zagazig, Egypt