APPROXIMATE SOLUTIONS OF FRACTIONAL BOUNDARY VALUE PROBLEMS BASED ON BETA FRACTIONAL DERIVATIVE

Year 2018, Volume: 30 Issue: 4, 478 - 486, 31.12.2018

Sebahat Ebru Daş

https://doi.org/10.7240/marufbd.440412

Abstract

In
this work, we consider some fractional differential equations with different
boundary conditions. Sinc-collocation method (SCM) has been employed to obtain
the approximate solution for these fractional boundary value problems (FBVPs).
Beta-derivative is taken for the fractional derivatives. Intercalarity, several
test samples with numerical simulations are handled. Convergence analysis shows
that SCM  is a consistent and effective
method.

Keywords

Sinc-collocation method, Beta-derivative, Fractional boundary value problem

BETA KESİRLİ TÜREVLİ SINIR DEĞER PROBLEMLERİNİN YAKLAŞIK ÇÖZÜMLERİ

Abstract

Bu çalışmada, bazı farklı sınır koşullu kesirli diferansiyel denklemleri ele aldık. Bu kesirli sınır değer problemlerinin için yaklaşık çözüm belirlemek için  Sinc sıralama yöntemi kullanılmıştır. Kesirli türevler için Beta türevi alınmıştır. Ek olarak, birtakım örnekler sayısal simulasyonları ile ele alınmıştır. Yakınsaklık analizi, Sinc sıralama yönteminin tuttarlı ve etkin bir yöntem olduğunu göstermiştir.

Keywords

Sinc sıralama yöntemi, Beta türevi, Kesirli sınır değer problemi

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