Ercan ÇELİK, Numan YALÇIN

Çarpımsal Cauchy-Euler ve Legendre Diferansiyel Denklemi

Bu çalışmada, klasik analizden değişken katsayılı lineer diferansiyel denklemlerin özel bir hali olan Cauchy-Euler diferansiyel denklemi ve Legendre diferansiyel denkleminin özellikleri baz alınarak; Çarpımsal analizde değişken üslü çarpımsal lineer diferansiyel denklemlerin özel bir hali olan çarpımsal Cauchy-Euler diferansiyel denklemi ve çarpımsal Legendre diferansiyel denkleminin tanımı verilmiş ve çözümleri incelenmiştir. Ayrıca çarpımsal mertebe düşürme metodu verilmiştir.

Anahtar Kelimeler:

Çarpımsal Türev, Çarpımsal Cauchy-Euler diferansiyel denklemi, Çarpımsal Legendre diferansiyel denklemi

Multiplicative Cauchy-Euler and Legendre Differential Equation

In this study, taking properties of Cauchy-Euler differential equation and Legendre differential equation, which are particular instances of linear differential equations with variable coefficients in classical analysis, as a basis, definitions of multiplicative Cauchy-Euler differential equation and multiplicative Legendre differential equation , which are types of multiplicative linear differential equations in multiplicative analysis, are given and also their solutions are investigated. In addition, multiplicative reduction of order method is given.

Keywords:

Multiplicative derivative, Multiplicative Cauchy-Euler differential equation, Multiplicative Legendre differential equation,

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