A new approach to the fractional Abel k-integral equations and linear fractional differential equations in a fuzzy environment
Küçük Resim Yok
Tarih
2024
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Elsevier
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
This paper introduces some recent approaches to the fuzzy fractional Abel integral equations with respect to another function, which is called the fuzzy fractional Abel k-integral equations. The problem proposed here allows for the interpolation of different types of fuzzy classical fractional Abel integral equations, and the solvability of each type of integral equation is also discussed. Additionally, a new approach to the linear fuzzy fractional differential equations in the space of generalized fuzzy functions is introduced. Unlike previous approaches with gH-differentiability, this approach avoids making any prior assumptions about the solution's monotonic behavior during the solving process. It also overcomes the problem of multiple solutions for fuzzy fractional differential equations. To demonstrate the benefits of this approach, two initial value problems of linear fuzzy differential equations are compared using two different concepts of fractional derivatives: the Caputo fractional gH-differentiability and the Caputo fractional derivative in the generalized fuzzy space. Furthermore, some applications are provided in a viscoelastic material model and a population growth with harvesting model.
Açıklama
Anahtar Kelimeler
The Fuzzy Fractional Abel K-Integral Equations, The Linear Fuzzy Fractional Differential Equations, The Generalized Fuzzy Space, Laplace-Like Transform, The Pade Approximation
Kaynak
Fuzzy Sets and Systems
WoS Q Değeri
N/A
Scopus Q Değeri
Q1
Cilt
481
