The General Fractional Integrals and Derivatives on a Finite Interval
Mathematics, 2023 The general fractional integrals and derivatives considered so far in the Fractional Calculus literature have been defined for the functions on the real positive semi-axis.
Mohammed Al-Refai, Yuri Luchko
doaj +2 more sources
General Fractional Integrals and Derivatives with the Sonine Kernels [PDF]
Mathematics, 2021 In this paper, we address the general fractional integrals and derivatives with the Sonine kernels on the spaces of functions with an integrable singularity at the point zero.
Yuri Luchko
doaj +2 more sources
Certain Hermite-Hadamard type inequalities via generalized k-fractional integrals [PDF]
Journal of Inequalities and Applications, 2017 Some Hermite-Hadamard type inequalities for generalized k-fractional integrals (which are also named ( k , s ) $(k,s)$ -Riemann-Liouville fractional integrals) are obtained for a fractional integral, and an important identity is established.
Praveen Agarwal +2 more
doaj +2 more sources
Fractional integrals inequalities for exponentially \(m\)-convex functions
, 2020 Fractional integrals inequalities for exponentially m-convex functions Sajid Mehmood1,∗ and Ghulam Farid1 1 Department of Mathematics, COMSATS University Islamabad, Attock Campus, Pakistan.; ghlmfarid@cuiatk.edu.pk(G.F) * Correspondence: smjg227@gmail ...
Sajid Mehmood, Ghulam Farid
openalex +2 more sources
General Fractional Integrals and Derivatives of Arbitrary Order [PDF]
Symmetry, 2021 In this paper, we introduce the general fractional integrals and derivatives of arbitrary order and study some of their basic properties and particular cases.
Yuri Luchko
semanticscholar +1 more source
Hermite-Hadamard, Trapezoid and Midpoint Type Inequalities Involving Generalized Fractional Integrals for Convex Functions [PDF]
Sahand Communications in Mathematical Analysis, 2023 We first construct new Hermite-Hadamard type inequalities which include generalized fractional integrals for convex functions by using an operator which generates some significant fractional integrals such as Riemann-Liouville fractional and the Hadamard
Hasan Kara, Samet Erden, Huseyin Budak
doaj +1 more source
fixed point, ψ-contraction, r-hybrid ψ-contraction, dynamic programming, integral equation
AIMS Mathematics, 2021 In this work, we establish inequalities of Hermite-Hadamard-Mercer (HHM) type for convex functions by using generalized fractional integrals. The results of our paper are the extensions and refinements of Hermite-Hadamard (HH) and Hermite-Hadamard-Mercer
Miguel Vivas-Cortez +3 more
doaj +1 more source
On new Milne-type inequalities for fractional integrals
Journal of Inequalities and Applications, 2023 In this study, fractional versions of Milne-type inequalities are investigated for differentiable convex functions. We present Milne-type inequalities for bounded functions, Lipschitz functions, functions of bounded variation, etc., found in the ...
H. Budak, Pınar Kösem, H. Kara
semanticscholar +1 more source
Novel results on trapezoid-type inequalities for conformable fractional integrals
Turkish Journal of Mathematics, 2023 : This paper establishes an identity for the case of differentiable s − convex functions with respect to the conformable fractional integrals. By using this identity, sundry trapezoid-type inequalities are proven by s − convex functions with the help of ...
F. Hezenci, H. Budak
semanticscholar +1 more source
Hermite-Hadamard-Mercer type inequalities for fractional integrals
Filomat, 2021 In the present note, we proved Hermite-Hadamard-Mercer inequalities for fractional integrals and we established some new fractional inequalities connected with the right and left-sides of Hermite-Hadamard-Mercer type inequalities for differentiable ...
Hatice Öğulmüş, Zeki Sarıkay
semanticscholar +1 more source