Results 71 to 80 of about 2,896 (148)

Fractional Representation Formulae Under Initial Conditions and Fractional Ostrowski Type Inequalities

Demonstratio Mathematica, 2015
Here we present very general fractional representation formulae for a function in terms of the fractional Riemann-Liouville integrals of different orders of the function and its ordinary derivatives under initial conditions.
Anastassiou George A.
doaj   +1 more source

A fractional Gauss–Jacobi quadrature rule for approximating fractional integrals and derivatives

, 2017
We introduce an efficient algorithm for computing fractional integrals and derivatives and apply it for solving problems of the calculus of variations of fractional order.
Babolian, E., S. Jahanshahi, Vahidi, A. R., Jahanshahi, S., Torres, D. F. M., E. Babolian, D.F.M. Torres, A.R. Vahidi   +7 more
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Further properties of Osler's generalized fractional integrals and derivatives with respect to another function [PDF]

, 2019
In this paper we discuss fractional integrals and fractional derivatives of a function with respect to another function. We present some fundamental properties for both types of fractional operators, such as Taylor’s theorem, Leibniz and semigroup ...
Almeida, Ricardo
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ON GENERALIZED FRACTIONAL INTEGRALS AND DERIVATIVES

, 2011
In this paper we present a generalization to two existing fractional integrals and derivatives, namely, the Riemann-Liouville and Hadamard fractional operators.
Katugampola, Don Udita Nalin
core  

Advances in Fractional Modeling and Computation

Fractal and Fractional
Fractional calculus, the study of derivatives and integrals of arbitrary order [...]
Yuri Dimitrov, Slavi Georgiev, Venelin Todorov, Jordan Hristov   +3 more
doaj   +1 more source

On Improved Simpson-Type Inequalities via Convexity and Generalized Fractional Operators

Journal of Mathematics
In this work, we develop novel Simpson-type inequalities for mappings with convex properties by employing operators for tempered fractional integrals. These findings expand upon and refine classical results, including those linked to Riemann–Liouville ...
Areej A. Almoneef, Abd-Allah Hyder, Fatih Hezenci, Hüseyin Budak   +3 more
doaj   +1 more source

Hardy type inequalities for fractional integrals and derivatives of Riemann–Liouville [PDF]

, 2017
© 2017, Pleiades Publishing, Ltd. We prove new Hardy type inequalities for Riemann–Liouville fractional integrals and derivatives in the case when the weight function have power and logarithmic ...
Nasibullin R., Nasibullin, Ramil
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New Extensions of the Hermite–Hadamard Inequality for Multiplicative Riemann–Liouville Fractional Integrals

Journal of Function Spaces
In this paper, new lower and upper bounds for the left and right sides of Hermite–Hadamard inequalities involving multiplicative Riemann–Liouville fractional integrals are established by using functions whose second-order multiplicative derivatives are ...
Hüseyin Budak, Büşra Betül Ergün, Ercan Çelik   +2 more
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Novel Ostrowski–Type Inequalities for Generalized Fractional Integrals and Diverse Function Classes [PDF]

In this work, novel Ostrowski-type inequalities for dissimilar function classes and generalized fractional integrals (FITs) are presented. We provide a useful identity for differentiable functions under FITs, which results in special expressions for ...
Hüseyin Budak, Hyder, Abd-Allah, Barakat, Mohamed A., Almoneef, Areej A., Budak, Huseyin, Mohamed A. Barakat, Areej A. Almoneef, Abd-Allah Hyder   +7 more
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Editorial for the Special Issue of Mathematics “Fractional Differential Equations, Inclusions and Inequalities with Applications II”

Mathematics
Within the field of fractional calculus, defined fractional derivatives and integrals within complex domains and their practical applications are frequently explored, and in recent years, this field has seen a significant rise in research interest [...]
Sotiris K. Ntouyas
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