Existence and Approximate Controllability of Mild Solutions for Hadamard-Type Fractional Systems in Banach Spaces
Indian Journal of Pure and Applied Mathematics, 2026 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Publication Date: 2026
- Doi Number: 10.1007/s13226-026-00962-2
- Journal Name: Indian Journal of Pure and Applied Mathematics
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, INSPEC, MathSciNet, zbMATH
- Keywords: Approximate controllability, Banach space, Hadamard fractional derivative, Krasnoselskii’s fixed point theorem, Logarithmic time scale, Mild solution, Weakly singular kernel
- Istanbul Gelisim University Affiliated: Yes
Abstract
This work establishes the approximate controllability of nonlinear Hadamard-type fractional systems with weakly singular logarithmic kernels in Banach spaces. Under suitable assumptions on the linearized control operator and a linear growth condition on the nonlinearity, we prove the existence of a mild solution steering the system from an arbitrary initial state arbitrarily close to a prescribed terminal state. The proof combines Krasnoselskii’s fixed point theorem with refined estimates involving logarithmic convolutions.