New Exact Solutions of Time Conformable Fractional Klein Kramer Equation

- Khaled Mohammed SAAD,
- A A Alderremy,
- H I Abdel-Gawad,
- Khaled M Saad,
- Shaban Aly

A A Alderremy

Department of Mathematics, Faculty of Science King, Kingdom of Saudi Arabia, Department of Mathematics, Faculty of Science, Khalid University, Department of Mathematics, Faculty of Science King, Kingdom of Saudi Arabia, Khalid University

H I Abdel-Gawad

Cairo University, Department of Mathematics, Faculty of Science, Cairo University

Khaled M Saad

Taiz University, Department of Mathematics, College of Arts and Sciences, Department of Mathematics, Faculty of Applied Science, Najran University, Department of Mathematics, Faculty of Applied Science, Taiz University, Department of Mathematics, College of Arts and Sciences, Najran University

Shaban Aly

Department of Mathematics, Faculty of Science, Al-Azhar University

## Abstract

The Klein Krames equation (KKE) stands for the probability distribution function (PDF) that describes the diffusion of particles subjected an external force. It is shown that 2 A. A. Alderremy, H. I. Abdel-Gawad, Khaled M. Saad, Shaban Aly the conformable fractional derivative (CFD) KKE can be reduced to the classical one's by using similarity transformations. Here, the objective of this work is to find the exact solutions of CFD-KKE.. To this issue, an approach is presented. It is based on transforming the KKE to a system of first order PDEs. The solutions are found by implementing extended unified method. It is found that, the integrability condition is that the external force is constant. The numerical results of the solutions are calculated and the are shown graphically. 2020 Mathematics Subject Classification: 34A08; 35A22; 41A30; 65N22.