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    Hardy-type inequalities within fractional derivatives without singular kernel
    (Springeropen, 2018) Başcı, Yasemin; Baleanu, Dumitru
    In this manuscript, we developed the Hardy-type inequality within the Caputo-Fabrizio fractional derivative. We presented some illustrative examples to confirm our work.
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    New aspects of Opial-type integral inequalities
    (Springeropen, 2018) Başcı, Yasemin; Baleanu, Dumitru
    In this manuscript, we prove new aspects for several Opial-type integral inequalities for the left and right Caputo-Fabrizio operators with nonsingular kernel. For this purpose we use the inequalities obtained by Andri et al. (Integral Transforms Spec. Funct. 25(4):324-335, 2014), which is the generalization of an inequality of Agarwal and Pang (Opial Inequalities with Applications in Differential and Difference Equations, 1995). Besides, examples are presented to validate the reported results.
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    On Hilbert-Pachpatte type inequalities within?-Hilfer fractional generalized derivatives
    (Amer Inst Mathematical Sciences-Aims, 2023) Başçı, Yasemin; Baleanu, Dumitru
    In this manuscript, we discussed various new Hilbert-Pachpatte type inequalities implying the left sided psi-Hilfer fractional derivatives with the general kernel. Our results are a generalization of the inequalities of Pecaric ' and Vukovic ' [1]. Furthermore, using the specific cases of the psi-Hilfer fractional derivative, we proceed with wide class of fractional derivatives by selecting psi, a1, b1 and considering the limit of the parameters alpha and beta.
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    Ostrowski type inequalities involving psi-Hilfer fractional integrals
    (Mdpi, 2019) Başcı, Yasemin; Baleanu, Dumitru
    In this study we introduce several new Ostrowski-type inequalities for both left and right sided fractional integrals of a function g with respect to another function psi. Our results generalized the ones presented previously by Farid. Furthermore, two illustrative examples are presented to support our results.