ON THE FINITE DELAYED FRACTIONAL DIFFERENTIAL EQUATION VIA THE WEIGHTED RIEMANN–LIOUVILLE DERIVATIVE OF VARIABLE ORDER
Fractals, vol.34, no.5, 2026 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 34 Issue: 5
- Publication Date: 2026
- Doi Number: 10.1142/s0218348x26500167
- Journal Name: Fractals
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Compendex, INSPEC, zbMATH
- Keywords: Fixed-Point Theorems, Initial Value Problems, Stability Analysis, Variable-Order Derivatives
- Istanbul Gelisim University Affiliated: Yes
Abstract
This study investigates the existence and uniqueness of solutions to initial value problems for nonlinear variable-order weighted fractional differential equations with finite delay. Building upon and generalizing prior constant-order fractional models, our approach employs fixed-point theory, specifically the Banach and Schauder fixed-point theorems, in suitable weighted function spaces to rigorously establish these fundamental results. We further demonstrate the applicability of our theoretical framework through illustrative examples. The findings contribute significantly to the mathematical understanding and modeling capabilities of complex systems exhibiting memory and hereditary properties governed by variable-order fractional dynamics.