Değişken Katsayılı Kesirli Mertebeden Diferansiyel Denklemler için Etkili bir Yöntem

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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