Abstract
AbstractThis paper focuses on exploring the existence of solutions for a specific class of FDEs by leveraging fixed point theorem. The equation in question features the Caputo fractional derivative of order $3<\hat{u} \leq 4$
3
<
u
ˆ
≤
4
and includes a term $\Theta (\beta,\mathscr{Z}(\beta ))$
Θ
(
β
,
Z
(
β
)
)
alongside boundary conditions. Through the application of a fixed point theorem in appropriate function spaces, we consider nonlocal conditions along with necessary assumptions under which solutions to the given FDE exist. Furthermore, we offer an example to illustrate the results.
Publisher
Springer Science and Business Media LLC
Reference21 articles.
1. Podlubny, I.: Fractional differential equations, mathematics in science and engineering (1999)
2. Le Mehaute, A., Crepy, G.: Introduction to transfer and motion in fractal media: the geometry of kinetics. Solid State Ion. 9, 17–30 (1983)
3. Faieghi, M., Kuntanapreeda, S., Delavari, H., Baleanu, D.: LMI-based stabilization of a class of fractional-order chaotic systems. Nonlinear Dyn. 72, 301–309 (2013)
4. Sokolov, I.M., Klafter, J., Blumen, A.: Fractional kinetics. Phys. Today 55(11), 48–54 (2002)
5. Kilbas, A.A., Marichev, O.I., Samko, S.G.: Fractional Integrals and Derivatives (Theory and Applications) (1993)