A Study on Tempered \((k,\psi)\)-Hilfer Fractional Operator
Keywords:
psi-Hilfer fractional derivative, k-generalized psi-Hilfer fractional derivative, tempered fractional operators, existence, uniquenessAbstract
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.
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