THEORY AND APPLICATIONS OF THE DOUBLE LAPLACE TRANSFORM FOR LOCAL DERİVATİVES WİTH THE MITTAG LEFFLER KERNEL

Year 2025, Volume: 25 Issue: 4, 774 - 784, 04.08.2025

Burak Özküçük , Erdal Baş

https://doi.org/10.35414/akufemubid.1569312

Abstract

This article aims to define the 𝑀-derivative double Laplace transform, which is the general form of the six-parameter conformable derivative involving the Mittag-Leffler function. It is expressed with several theorems and will give us a useful and dependable method for solving fractional 𝑀-derivative partial differenial equations. Furthermore, the application of these given definitions and theorems to fractional partial differential equations is shown. Finding solutions to partial differential equations containing 𝑀-derivatives that can match mathematical, engineering, and physical mode ls may be accomplished with the use of this transformation.

Keywords

M-derivative, Laplace transform, Double M-Derivative, Truncated Mittag-Leffler function

MİTTAG LEFFLER ÇEKİRDEĞİ İLE LOKAL TÜREVLER İÇİN ÇİFT KATLI LAPLACE DÖNÜŞÜMÜ TEORİSİ VE UYGULAMALARI

Abstract

Bu makale, Mittag-Leffler fonksiyonunu içeren altı parametreli uyumlu türevin genel formu olan M-türevi çift katlı Laplace dönüşümünü tanımlamayı amaçlamaktadır. Birkaç teoremle ifade edilir ve bize M-türevi kısmi diferansiyel denklemleri çözmek için kullanışlı ve güvenilir bir yöntem verecektir. Ayrıca, verilen bu tanım ve teoremlerin kesirli kısmi diferansiyel denklemlere uygulanması gösterilmiştir. Matematiksel, mühendislik ve fiziksel modellerle eşleşebilecek M-türevlerini içeren kısmi diferansiyel denklemlere çözümler bulmak, bu dönüşümün kullanılmasıyla gerçekleştirilebilir.

Keywords

M-türev, Laplace dönüşümü, İki katlı M- Laplace dönüşümü, Mattag Leffler fonksiyonu

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