Kesirli Diferansiyel Sistemler için Verilen Bazı Sınır Koşullarında Çözümlerin Varlığı ve Tekliği

Öz

Bu makalede, periyodik problemlerin kesirli durumu tartışılmaktadır. Zaman kesirli ısı denklemi göz önünde bulundurularak, periyodik ve anti-periyodik sınır koşulları ile ters problemler oluşturulmuştur. Bu problemler için varlık ve teklik sonuçlarını elde etmek için Fourier yöntemi kullanılmıştır. Periyodik bir fonksiyonun kesirli türevi gerçek eksen boyunca analiz edilmiş ve lineer sistemlerin kesirler durumundaki periyodik davranışı araştırılmıştır.

Anahtar Kelimeler

• Periyodik
• Anti-periyodik
• Kesirli Türev
• Fourier Metodu
• Lineer Sistem

Existence and Uniqueness of Solutions in Some Boundary Conditions for Fractional Differential Systems

Abstract

In this article, fractional case of periodic problems is discussed. Considering the time fractional heat equation, inverse problems with periodic and anti-periodic boundary conditions were created. For these problems, the Fourier method was used to obtain existence and uniqueness results. The fractional derivative of a periodic function was analyzed along the real axis, and the periodic behavior of linear systems in case of fractions was investigated.

Keywords

• Periodic
• Anti-periodic
• Fractional Derivative
• Fourier Method
• Linear System

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