Zaman Skalasında Oransal Öğrenme ve Unutma Modellerinin Oransal Laplace Dönüşümü ile Çözümleri

Year 2024, Volume: 36 Issue: 1, 1 - 10, 28.03.2024

Ayşe Çiğdem Yar Emrah Yılmaz

Abstract

Bilgi, bazı faaliyetler sonucunda kazanılır ancak zamanla unutulur. Matematik, mühendislik ve psikoloji gibi alanlarda bu konu üzerine pek çok çalışma yapılmıştır. Literatürde pek çok öğrenme ve unutma modeli bulunmaktadır. Bu çalışmada, klasik analizde ele alınan bir öğrenme ve unutma modeli, zaman skalasında oransal türev yardımıyla yeniden tanımlanmıştır. Öğrenme ve unutma oranlarının sabit olduğu ve öğrenme fonksiyonunun üstel ve hiperbolik fonksiyon özellikleri gösterdiği durumlar analiz edilmiştir. Bu modeller oransal Laplace dönüşümü yardımıyla çözülmektedir. Son olarak birinci mertebeden oransal dinamik denklemlerin genel çözüm yöntemi ile ele alınan modeler zaman skalasında incelenmiştir.

Keywords

Oransal türev, oransal Laplace dönüşümü, zaman skalası, öğrenme ve unutma modeli

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

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

Proportional derivative, proportional Laplace transform, time scale, learning and forgetting model

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