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March  2020, 13(3): 881-888. doi: 10.3934/dcdss.2020051

## Inclusion of fading memory to Banister model of changes in physical condition

 1 Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 28095, Riyadh 11437, Saudi Arabia 2 Department of mathematics, AMITY School of Engineering and Technology, AMITY University Rajasthan, Jaipur -302022, India 3 Nature Science Department, Community College of Riyadh, King Saud University, P.O. Box 28095, Riyadh 11437, Saudi Arabia 4 Department of Mathematics, Faculty of Science, Fayoum University, Fayoum, Egypt

* Corresponding author: Ravi Shanker Dubey

Received  May 2018 Revised  June 2018 Published  March 2019

Fund Project: The authors would like to extend their appreciation to the Deanship of Scientific Research at King Saud University for funding this work through research group No (RG-1438-086).

We introduced the fading memory effect to the model portraying the prediction in physical condition. The classical model is known as the Banister model. We presented the existence and uniqueness conditions of the exact solutions of this model using three different memory including the bad memory induces by the power law and the good memories induced by exponential decay law and the Mittag-Leffler law. We derived the exact solutions using the Laplace transform for the non-delay version.

Citation: Mansour Shrahili, Ravi Shanker Dubey, Ahmed Shafay. Inclusion of fading memory to Banister model of changes in physical condition. Discrete & Continuous Dynamical Systems - S, 2020, 13 (3) : 881-888. doi: 10.3934/dcdss.2020051
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