New Caputo fractional differential equation of higher order on unbounded interval and solvability in the Hölder space C0,q(Ω)
Journal of Inequalities and Applications, vol.2026, no.1, 2026 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 2026 Issue: 1
- Publication Date: 2026
- Doi Number: 10.1186/s13660-026-03456-1
- Journal Name: Journal of Inequalities and Applications
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH, Directory of Open Access Journals
- Keywords: Darbo’s fixed point theorem, Fractional boundary value problem, Hölder space, Measures of noncompactness
- Uşak University Affiliated: Yes
Abstract
We define a new Caputo fractional differential equation of higher-order on unbounded interval (Formula presented.) Also, we introduce a new family of measures of noncompactness in Hölder space C0,q(Ω) and we state a version of fixed point theorem of Darbo’s type. Then we study the existence of solutions of new Caputo fractional differential equation in Hölder space by using version of Darbo’s fixed point theorem associated with this new measure of noncompactness. An example is given to demonstrate application of our results.