Fractional approach for multi-dimensional wave-like equations with variable coefficient using an efficient method

Abstract

In this paper, we study multi-dimensional wave-like equations with variable coefficients within the frame of the fractional calculus using fractional natural decomposition method (FNDM). The considered algorithm is an elegant combination of natural transform and decomposition scheme. Five different cases are considered to illustrate and validate the competence of the projected technique in the present framework. The behaviours of the obtained results have been captured for diverse fractional order. To present the reliability and exactness of the FNDM, the numerical study has been presented. The achieved consequences illuminate that, the projected technique is very effective to analyse and easy to employ to investigate the nature of fractional nonlinear coupled system exemplifying the real-world problems.

Keywords

• Fractional wave-like equations
• Caputo Derivative
• fractional natural decomposition method

Değişken katsayılı çok boyutlu dalga benzeri denklemler için kesirli yaklaşım üzerine etkili bir metot

Abstract

Bu çalışmanın temel amacı, fraksiyonel doğal ayrıştırma yöntemini (FNDM) kullanarak kesirli operatör çerçevesinde değişken katsayılı çok boyutlu dalga benzeri denklemleri incelemektir. Değerlendirilen algoritma, doğal dönüşüm ve ayrıştırma şemasının güzel bir kombinasyonudur. Mevcut çerçevede öngörülen tekniğin yeterliliğini göstermek ve doğrulamak için beş farklı durum ele alınmıştır. Elde edilen sonuçların davranışları, çeşitli kesirli sıralar için değerlendirilmiştir. FNDM'nin güvenilirliğini ve kesinliğini göstermek için sayısal çalışma sunulmuştur. Elde edilen sonuçlar, öngörülen tekniğin analiz edilmesinin çok etkili olduğunu ve gerçek dünya problemlerini örnekleyen kesirli doğrusal olmayan bağlı sistemin doğasını araştırmak için kullanılmasının kolay olduğunu göstermektedir.

Keywords

• Kesirli dalga benzeri denklemler
• Caputo türevi
• kesirli doğal ayrıştırma yöntemi

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