Değişken Katsayılı Kesirli Mertebeden Diferansiyel Denklemler için Etkili bir Yöntem

Year 2019, Issue: 16, 205 - 210, 31.08.2019

Arzu Turan Dincel

Abstract

Bu çalışmada, değişken katsayılı kesirli diferansiyel denklemlerin çözümü için Bernoulli wavelet yaklaşımını öneriyoruz. Önerilen yöntemde, kesirli mertebeden integrasyonun operasyonel matrisi türetilir ve bu diferansiyel denklemin bir cebirsel denklem sistemine indirgenmesi sağlanır. Kesirli mertebeden integrasyonun operasyonel matrisi block pulse fonksiyonları ile elde edilir. Açıklayıcı örnekler sunulmaktadır. Örnekler, yöntemin doğru ve verimli olduğunu göstermektedir.

Keywords

Bernoulli wavelet, , Değişken Katsayılı Kesirli Mertebeden Diferansiyel denklemler

Efficient Method for the Solution of Fractional-order Differential Equations with Variable Coefficients

Abstract

In this paper, we propose the Bernoulli wavelet
approximation for the solution of the fractional differential
equations with variable coefficients. In the proposed method, the fractional
derivatives are transformed using the operational matrix of fractional order
integration and by doing that differential equation reduces to a system of
algebraic equations. The operational matrix of fractional order integration is
obtained via block pulse functions. Illustrative examples are presented. The
examples demonstrate that the method is accurate and efficient.

Keywords

Bernoulli wavelet, Fractional-order differential equations with variable coefficients, Caputo derivative

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