Solvability of Fractional Boundary Value Problems for a Combined Caputo Derivative

Toprakseven Ş.

Konuralp Journal of Mathematics, cilt.9, sa.1, ss.119-126, 2021 (Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 9 Sayı: 1
  • Basım Tarihi: 2021
  • Dergi Adı: Konuralp Journal of Mathematics
  • Derginin Tarandığı İndeksler: Scopus
  • Sayfa Sayıları: ss.119-126
  • Anahtar Kelimeler: Combined Caputo derivative, Existence, Fixed point
  • Yozgat Bozok Üniversitesi Adresli: Evet

Özet

This paper deals with a class of boundary value problems of fractional differential equations involving the combined Caputo derivative, which can reflect both the past and the future nonlocal memory effects. This fractional derivative is a convex combination of the left and right Caputo fractional derivative of different order. By using the fractional Gronwall-type inequalities and some fixed point theorems, we have established some sufficient conditions for the existence and uniqueness of solutions for fractional boundary value problems with the combined Caputo fractional derivative. Various examples are given to illustrate the applications of the results.