Existence and Uniqueness of C(n)-(ω, c)-Periodic Mild Solutions to Some Two-Term Fractional Evolution Equations
Méthode Koyabanda1 and Gaston M. N'Guérékata2
1Department of Mathematics and Computer Science, University of Bangui, CAR
2NEERLab, Department of Mathematics, Morgan State University, Baltimore, MD 21251, USA
Received on September 19, 2026
Accepted on October 7, 2026
Communicated by Maximilian F. Hasler
| Abstract. In this paper, we establish some new properties of C(n)-(ω, c)-periodic functions, then we apply them to study the existence and uniqueness of mild solutions of these types to the following linear fractional differential equations cDtα u(t) = Au(t) + cDtα−1 f(t), 1 < α < 2, t ∈ ℝ, and the semilinear case cDtα u(t) = A u(t) + cDtα−1 g(t, u(t)), 1 < α < 2, t ∈ ℝ, where cDtα(·) (1 < α < 2) stands for the Caputo derivative and A is a linear densely defined operator of sectorial type on a complex Banach space X, and the functions f and g are C(n)-(ω, c)-periodic. Our results are obtained using the Leray-Schauder alternative theorem, the Banach fixed point principle and the Schauder theorem. | |
| Keywords: | Banach space; Leray-Schauder alternative theorem; Arzelà-Ascoli theorem; two-term fractional evolution equation; Krasnoselskii's theorem; C(n)-(ω, c)-periodic functions; mild solutions. |
| 2010 Mathematics Subject Classification: 35B10, 46E15, 47D06, 47J35, 93D22. | |
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