Conformable Anlamında Kesirli Mertebeden Fokker-Planck Denkleminin Analitik Çözümü

Bu çalışmada, istatistiksel fizikte önemli bir role sahip olan doğrusal olmayan kesirli Fokker Planck (FP) denklemi, yeni tanımlanmış olan conformable Laplace ayrıştırma metodu (CLAM) ile ilk kez çözülmektedir. Bu yeni algoritma, conformable Laplace dönüşümü ile Adomian ayrıştırma yöntemini birleştirmektedir. Çalışmamızda ilk olarak, kesirli türevin bazı temel tanımları ve teoremleri conformable anlamında verilmiştir. Ardından CLAM’ ın genel algoritması anlatılmıştır. Bundan sonra, kullanılan metot grafikler yardımıyla sayısal örnekle verilerek desteklenmiştir. Sayısal örnekten görüldüğü üzere, conformable Laplace ayrıştırma yöntemi güçlü, güvenilir, kullanımı kolay ve kesirli mertebeden çok çeşitli kısmi türevli diferensiyel denklemlere uygulanabilir özelliklere sahiptir

Anahtar Kelimeler:

conformable fractional derivative, Laplace decomposition method, Fokker Planck equation

An Analytical Solution to Conformable Fractional Fokker-Planck Equation

It is the first time in this work that a newly defined conformable Laplace decomposition method (CLDM) is applied to nonlinear fractional Fokker Planck (FP) equation which has a major role in statistical physics. This new algorithm combines conformable Laplace transform and Adomian decomposition method. First, some basic theorems and definitions of fractional derivative are given in conformable sense. Then, the general algorithm of CLDM is presented. After that, the presented method is supported by numerical example by the aid of figures. As is seen from the numerical example, conformable Laplace decomposition method is strong, easy to use, reliable and applicable to a wide variety of fractional PDEs.

Keywords:

conformable fractional derivative, Laplace decomposition method, Fokker Planck equation,

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