On the Caputo-Hadamard fractional IVP with variable order using the upper-lower solutions technique
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Tarih
2023
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Amer Inst Mathematical Sciences-Aims
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
This paper studies the existence of solutions for Caputo-Hadamard fractional nonlinear differential equations of variable order (CHFDEVO). We obtain some needed conditions for this purpose by providing an auxiliary constant order system of the given CHFDEVO. In other words, with the help of piece-wise constant order functions on some continuous subintervals of a partition, we convert the main variable order initial value problem (IVP) to a constant order IVP of the Caputo-Hadamard differential equations. By calculating and obtaining equivalent solutions in the form of a Hadamard integral equation, our results are established with the help of the upper-lower-solutions method. Finally, a numerical example is presented to express the validity of our results.
Açıklama
Anahtar Kelimeler
fractional variable order, Caputo-Hadamard fractional derivative, upper-lower solutions, existence results
Kaynak
Aims Mathematics
WoS Q Değeri
Q1
Scopus Q Değeri
Q1
Cilt
8
Sayı
3
