An Efficient Method for Numerical Solution of Fractional Pantograph Equations

Öz

The pantograph differential equation is one of the most well-known delay differential equations. There are many different pantograph equations in quantum mechanics. In this study, we present Legendre - spectral method for solving fractional pantograph equations help of Caputo derivative. The aim of this method's approach is that it induces such problems to solving a system of algebraic equation, thus greatly simplifying the problem. The proposed method is extremely successful and effective in solving fractional pantograph equations. All of examples are solved help of the Maple and MATLAB.

Anahtar Kelimeler

• Shifted Legendre polynomials
• spectral method
• pantograph equation
• Caputo fractional derivative

Kesirli Pantograf Denklemlerinin Nümerik Çözümleri için Etkili Yöntemler

Öz

Pantograf diferansiyel denklemi iyi bilinen gecikmeli diferansiyel denklemlerden biridir. Kuantum mekaniğinde birçok farklı pantograf denklemleri kullanılmaktadır. Bu çalışmada, Caputo kesirli türevi yardımıyla kesirli pantograf diferansiyel denklemlerini çözmek için Legendre - spektral yöntemi uygulanmıştır. Bu yöntem ile, denklemi çözmek için cebirsel bir denklem sistemi oluşturularak, problemi büyük ölçüde basitleştirmek amaçlanmaktadır. Spectral yöntemler, kesirli pantograf denklemlerini çözmede son derece başarılı ve etkilidir. Bu çalışmadaki problemler Maple ve Matlab programları yardımıyla çözülmüştür.

Anahtar Kelimeler

• Ötelenmiş Legendre polinomları
• spektral metot
• pantograf denklemi
• Caputo kesirli türevi

Kaynakça

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