Solutions of Proportional Learning and Forgetting Models by Proportional Laplace Transform on Time Scales

Authors : Ayşe Çiğdem Yar, Emrah Yılmaz

Pages : 1-10

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Publication Date : 2024-03-28

Article Type : Research Paper

Abstract :Knowledge is acquired as a result of some activities but is forgotten over time. Much work has been done on this subject in fields such as mathematics, engineering and psychology. There are many learning and forgetting models in literature. In this study, a learning and forgetting model considered in classical analysis is redefined with the help of proportional derivative on time scales. The cases where the learning and forgetting rates are constant and the Araştırma Makalesi Araştırma Makalesi learning function shows exponential and hyperbolic functions properties are analyzed. These models are solved with the help of the proportional Laplace transform. Finally, the models considered with the general solution method of first-order proportional dynamic equations were examined on the time scale.
Keywords : Oransal türev, oransal Laplace dönüşümü, zaman skalası, öğrenme ve unutma modeli

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