HÜLYA DURUR, MEHMET ŞENOL, Ali KURT, Orkun TAŞBOZAN

Approximate Solutions of the Time-Fractional Kadomtsev-Petviashvili Equation with Conformable Derivative

In this study, residual power series method, namely RPSM, is applied to solve time-fractional Kadomtsev-Petviashvili (K-P) differential equation. In the solution procedure, the fractional derivatives are explained in the conformable sense. The model is solved approximately and the obtained results are compared with exact solutions obtained by the sub-equation method. The results reveal that the present method is accurate, dependable, simple to apply and a good alternative for seeking solutions of nonlinear fractional partial differential equations.

Anahtar Kelimeler:

Kesirli kısmi diferansiyel denklemler, Kesirli Kadomtsev-Petviashvili denklemi, conformable kesirli türev

Zaman-Kesirli Kadomtsev- Petviashvili Denkleminin Conformable Türev ile Yaklaşık Çözümleri

Bu çalışmada, zaman-kesirli Kadomtsev-Petviashvili (K-P) diferansiyel denklemini çözmek için Rezidual Kuvvet Serisi Metodu (RPSM) kullanılmıştır. Çözüm prosedüründe, kesirli türevler, conformable kesirli türev tanımına göre hesaplanmıştır. Bu model yaklaşık olarak çözülmüş ve elde edilen sonuçlar, sub-equation metodu ile elde edilen tam çözümlerle karşılaştırılmıştır. Sonuçlar, mevcut yöntemin doğru, güvenilir, uygulanmasının basit olduğunu ve doğrusal olmayan kısmi diferansiyel denklemlerin çözümü için iyi bir alternatif olduğunu ortaya koymaktadır.

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