Mittag-Leffler Function in different areas of life

Abstract

In this work, Mittag-Leffler (ML) function that is encountered in different solutions of fractional kinetic equation and generalizes exponential function has been handled. With the help of ML function, growth dynamics of population, foreign trade volume and greenhouse gas emission have been investigated. With this manner, graphical representations for these processes have been compared with real data. The harmony between theory and real data has been investigated with the help of order of fractional derivative.

Keywords

• Mittag-Leffler Function
• Fractional Calculus
• Memory Effect

Yaşamın Farklı Alanlarında Mittag-Leffler Fonksiyonu

Öz

Bu çalışmada kesirsel kinetik denklemin farklı çözümlerinde karşımıza çıkan ve eksponansiyel fonksiyonu genelleyen Mittag-Leffler (ML) fonksiyonu ele alınmaktadır. ML fonksiyonu yardımıyla nüfus, sera gazı salınımı ve dış ticaret hacmi süreçlerindeki artma dinamikleri incelenmektedir. Bu amaçla bu süreçler için grafiksel gösterimler yapılmakta ve gerçek veriler ile karşılaştırılmaktadır. Kesirsel türev mertebesi yardımıyla gerçek değerler ile teorik hesaplamaların arasındaki uyum incelenmektedir.

Anahtar Kelimeler

• Mittag-Leffler fonksiyonu
• Kesirsel matematik
• Bellek etkisi

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