B. Rachid
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New Definition of $\mathcal{N}^{\alpha}_F$-Sumudu conformable transform
Bahloul Rachid, Rachad Houssame
MFAT 31 (2025), no. 4, 336-343
336-343
Using the new definition of the $\mathcal{N}^{\alpha}_F$-derivative function introduced by Juan E. Nápoles Valdés and al. (2020), we provide a new definition for the $\mathcal{N}^{\alpha}_F$-Sumudu transform, $\mathcal{N}^{\alpha}_F$-Sumudu conformable transform. Additionally, we establish several important results related to these new transforms. We also give a new definition of convolution related to this $\mathcal{N}^{\alpha}_F$-derivative and we show that it is commutative and associative.
$\mathcal{N}^{\alpha}_F$-fractional semi-groups of operators
Bahloul Rachid, Rachad Houssame, Thabet Abdeljawad
MFAT 31 (2025), no. 1, 39-46
39-46
Based on the new definition of the $\mathcal{N}^{\alpha}_F$-derivative function introduced by Juan E. Nápoles Valdes et al. (2020) in [1], we give a new definition and some results of the $\mathcal{N}^{\alpha}_F$-fractional semi-groups of operators.