Results 51 to 60 of about 2,896 (148)

Hermite–Hadamard-Type Inequalities for Convex Functions via the Fractional Integrals with Exponential Kernel

Mathematics, 2019
In this paper, we establish three fundamental integral identities by the first- and second-order derivatives for a given function via the fractional integrals with exponential kernel.
Xia Wu, JinRong Wang, Jialu Zhang
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On an Inequality of H. G. Hardy

Journal of Inequalities and Applications, 2010
We state, prove, and discuss new general inequality for convex and increasing functions. As a special case of that general result, we obtain new fractional inequalities involving fractional integrals and derivatives of Riemann-Liouville type ...
Krulić Kristina, Iqbal Sajid, Pečarić Josip   +2 more
doaj  

Positive Solutions for a System of Coupled Semipositone Fractional Boundary Value Problems with Sequential Fractional Derivatives

Mathematics, 2021
We study the existence and multiplicity of positive solutions for a system of Riemann–Liouville fractional differential equations with sequential derivatives, positive parameters and sign-changing singular nonlinearities, subject to nonlocal coupled ...
Johnny Henderson, Rodica Luca, Alexandru Tudorache   +2 more
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Statistical Distribution Theory and Fractional Calculus

Stats
This is an overview paper. This paper is an attempt to show that fractional calculus can be reached through statistical distribution theory. This paper brings together results on fractional integrals and fractional derivatives of the first and second ...
A. M. Mathai
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Fractional Calculus of Variations in Terms of a Generalized Fractional Integral with Applications to Physics

Abstract and Applied Analysis, 2012
We study fractional variational problems in terms of a generalized fractional integral with Lagrangians depending on classical derivatives, generalized fractional integrals and derivatives.
Tatiana Odzijewicz, Agnieszka B. Malinowska, Delfim F. M. Torres   +2 more
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Algebraic Approach to the Fractional Derivatives

, 2004
In this paper we introduce an alternative definition of the fractional derivatives and also a characteristic class of so called ideal functions, which admit arbitrary fractional derivatives (also integrals)
Trenčevski, Kostadin, Tomovski, Živorad   +1 more
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On fractional derivatives with generalized Mittag-Leffler kernels

Advances in Difference Equations, 2018
Fractional derivatives with three parameter generalized Mittag-Leffler kernels and their properties are studied. The corresponding integral operators are obtained with the help of Laplace transforms.
Thabet Abdeljawad, Dumitru Baleanu
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A Review of Definitions for Fractional Derivatives and Integral [PDF]

, 2014
This paper presents a review of definitions of fractional order derivatives and integrals that appear in mathematics, physics, and ...
Machado, José António Tenreiro, Oliveira, Edmundo Capelas de, Machado, J. A. Tenreiro   +2 more
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Generalized Fractional ρ,k,φ-Proportional Hilfer Derivatives and Some Properties

Journal of Mathematics
Building on previous work in fractional calculus, this paper introduces new definitions for the ρ,k,φ-proportional integral and ρ,k,φ-proportional H fractional derivative.
Haihua Wang
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An Expansion Formula with Higher-Order Derivatives for Fractional Operators of Variable Order

The Scientific World Journal, 2013
We obtain approximation formulas for fractional integrals and derivatives of Riemann-Liouville and Marchaud types with a variable fractional order. The approximations involve integer-order derivatives only. An estimation for the error is given.
Ricardo Almeida, Delfim F. M. Torres
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