KESİRLİ MERTEBELİ DİFERANSİYEL DENKLEMLERİN YENİ SAYISAL ÇÖZÜMLERİ

Year 2024, , 43 - 52, 29.06.2024

Mehmet Ali Akınlar

https://doi.org/10.46460/ijiea.1459659

Abstract

Kesirli stokastik diferansiyel denklemler, çok çeşitli mühendislik ve bilimsel olguları simüle etmek için yaygın olarak kullanılan araçlardır. Bu makalede, belirsiz katsayılar yaklaşımının çeşitli kesirli stokastik modellere uygulanabilirliği incelenmiştir. Bu modeller kesirli beyaz gürültü terimine sahiptir ve çoğunlukla kesirli dereceli türev operatörleri tarafından üretilir. Ayrıca polinom kaos algoritmasının stokastik Lotka-Volterra ve Benney sistemlerine uygulamalarını da araştırıyoruz. Kesirli stokastik denklemler, çok çeşitli bilimsel ve mühendislik problemleri için model olarak işlev görme potansiyeline sahip tamamen yeni sistemlerdir. Bu makalede Galerkin tipi yaklaşımların etkin kullanımından ve belirsizlik veya gürültü terimi içeren kesirli dereceli sistemlere uygulanabilirliği araştırılmıştır.

Keywords

Galerkin yöntemleri, sayısal çözümler, skokastik sistemler, kesirli operatörler

NUMERICAL SOLUTIONS TO THE STOCHASTIC SYSTEMS WITH FRACTIONAL OPERATORS

Abstract

Fractional-stochastic differential equations are widely used tools to simulate a wide - range of engineering and scientific phenomena. In this paper, the applicability of the approach of indeterminate coefficients to various fractional-stochastic models is examined. These models have a fractional white noise term and are mostly produced by fractional-order derivative operators. We also investigate applications of a polynomial chaos algorithm to stochastic Lotka-Volterra and Benney systems. Fractional-stochastic equations are entirely novel systems that have the potential to function as models for a wide range of scientific and engineering phenomena. It is noted that fractional-order systems with uncertainty or a noise term can benefit from the effective use of Galerkin-type approaches in this article.

Keywords

The Galerkin method,, Numerical Solutions, Fractional-Stochastic Differential Equations,

Ethical Statement

Ethics committee approval document is not required for this study.

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