A Unified Approach to Implicit Fractional Differential Equations with Anti-Periodic Boundary Conditions

Ricardo Almeida ()
Additional contact information
Ricardo Almeida: Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal

Mathematics, 2025, vol. 13, issue 17, 1-20

Abstract: This paper develops a unified analytical framework for implicit fractional differential equations subject to anti-periodic boundary conditions. The study considers two main cases: fractional derivatives of order α ∈ ( 0 , 1 ) and α ∈ ( 1 , 2 ) , both defined with respect to a general kernel function. The existence and uniqueness of solutions are established using Banach’s and Schaefer’s fixed-point theorems under suitable Lipschitz conditions. Furthermore, Ulam–Hyers stability and generalized Ulam–Hyers stability are investigated for each problem. Examples are provided to illustrate the applicability of the main results.

Keywords: fractional calculus; implicit fractional differential equation; anti-periodic boundary conditions; Ulam–Hyers stability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/13/17/2890/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/17/2890/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:13:y:2025:i:17:p:2890-:d:1744054

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().