Kesirli mertebeden sınır değer problemlerini çözmek için bir sıralama yöntemi

Bu makalede sinc sıralama yöntemi, uyumlu kesirli türev içeren ikinci mertebeden kesirli sınır değer problemlerinin çözümünü elde etmek için kullanıldı. Bu amaçla sinc baz fonksiyonlarının kesirli türevlerini içeren terimleri ifade etmek için bir teorem ispat edildi. Yöntemin etkinliğini ve doğruluğunu göstermek için bazı problemler çözüldü ve elde edilen çözümler diğer sayısal yöntemler kullanılarak elde edilen yaklaşık çözümler ve problemlerin tam çözümleri ile karşılaştırıldı.

Anahtar Kelimeler:

Kesirli mertebeden diferansiyel denklemler

A collocation method for solving boundary value problems of fractional order

In this paper, the sinc collocation method is used to obtain the solution of the second-order fractional boundary value problems based on the conformable fractional derivative. For this purpose a theorem is proved to represent the terms having fractional derivatives in terms of sinc basis functions. To show the efficiency and accuracy of the present method, some problems are solved and the obtained solutions are compared with the approximate solutions obtained by using the other numerical methods as well as the exact solutions of the problems.

Keywords:

Differential equations of fractional order boundary value problems,

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