A Study on Tempered \((k,\psi)\)-Hilfer Fractional Operator
Abdelkrim Salım, Mouffak Benchohra · Letters in Nonlinear Analysis and its Applications · 2023
This paper introduces novel definitions of the tempered $(k,\psi)$-fractional operators and establishes their various properties. Our research focuses on applying these new findings to investigate the existence and uniqueness of solutions for a specific class of initial value problems concerning implicit nonlinear fractional differential equations and tempered $(k,\psi)$-Hilfer fractional derivative with nonlocal condition. To achieve this, we rely on the application of pertinent fixed-point theorems. Moreover, we offer illustrative examples to showcase the practical effectiveness of our main results.