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Open AccessMore properties of the proportional fractional integrals and derivatives of a function with respect to another function
In this article, we present some new properties of the fractional proportional derivatives of a function with respect to a certain function. We use a modified Laplace transform to find the relation between the...
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Article
Open AccessNew quantum estimates in the setting of fractional calculus theory
In this article, the investigation is centered around the quantum estimates by utilizing quantum Hahn integral operator via the quantum shift operator ψ q η ( ζ ) = q ζ + ( 1 − q ) η ${}_{\eta}\psi_{\math...
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Open AccessSome new local fractional inequalities associated with generalized \((s,m)\) -convex functions and applications
Fractal analysis is one of interesting research areas of computer science and engineering, which depicts a precise description of phenomena in modeling. Visual beauty and self-similarity has made it an attract...
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Open AccessCertain new weighted estimates proposing generalized proportional fractional operator in another sense
The present work investigates the applicability and effectiveness of generalized proportional fractional integral ( GPFI \(\mathcal{GPFI}\) ) operator in another sense. We aim to derive novel weighted generalizat...
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Open AccessSome new Simpson-type inequalities for generalized p-convex function on fractal sets with applications
The present article addresses the concept of p-convex functions on fractal sets. We are able to prove a novel auxiliary result. In the application aspect, the fidelity of the local fractional is used to establish...
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Open AccessNew fractional approaches for n-polynomial P-convexity with applications in special function theory
Inequality theory provides a significant mechanism for managing symmetrical aspects in real-life circumstances. The renowned distinguishing feature of integral inequalities and fractional calculus has a solid ...
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Open AccessIntegral inequalities via Raina’s fractional integrals operator with respect to a monotone function
We establish certain new fractional integral inequalities involving the Raina function for monotonicity of functions that are used with some traditional and forthright inequalities. Taking into consideration t...