Existence and Uniqueness Results for Fractional Differential Equations with Delay

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Duman O., Develi F.

1st INTERNATIONAL SYMPOSIUM ON RECENT ADVANCES IN FUNDAMENTAL AND APPLIED SCIENCES (ISFAS-2021), Erzurum, Türkiye, 10 - 12 Eylül 2021, ss.144

  • Yayın Türü: Bildiri / Özet Bildiri
  • Basıldığı Şehir: Erzurum
  • Basıldığı Ülke: Türkiye
  • Sayfa Sayıları: ss.144
  • Yıldız Teknik Üniversitesi Adresli: Evet

Özet

Fractional differential equations appear in various fields. For examples, it’s handled  in engineering with physical processes such as thermodynamics, polymer rheology, and mechanics as well as control theory and technical sciences like biophysics. The biggest factor in fractional differentiations being more popular than classical ones lately is that it is effective in explaining real-world problems.  But since there is no general technique for  obtaining  solutions of the dynamic systems specified by fractional calculus, existence and uniqueness theorems have an important place in the literature. In this paper we investigate the existence and uniqueness of solutions for the following fractional order differential equation

                                

cD^alpha is the fractional derivative of order  in the sense of Caputo.


Joint work with Faruk Develi, fdeveli@yildiz.edu.tr, Yildiz Technical University