Fractional variational problems with the Riesz-Caputo derivative [PDF]
, 2012 In this paper we investigate optimality conditions for fractional variational problems, with a Lagrangian depending on the Riesz-Caputo derivative. First we prove a generalized Euler-Lagrange equation for the case when the interval of integration of the ...
Almeida, R., Ricardo Almeida
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Taylor’s Formula for Generalized Weighted Fractional Derivatives with Nonsingular Kernels
Axioms, 2022 We prove a new Taylor’s theorem for generalized weighted fractional calculus with nonsingular kernels. The proof is based on the establishment of new relations for nth-weighted generalized fractional integrals and derivatives. As an application, new mean
Houssine Zine +3 more
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Modelling solute transport in soil columns using advective-dispersive equations with fractional spatial derivatives [PDF]
, 2010 Solute transport in soils is commonly simulated with the advective–dispersive equation, or ADE. It has been reported that this model cannot take into account several important features of solute movement through soil.
San Jose Martinez, Fernando
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Operational Calculus for the General Fractional Derivatives of Arbitrary Order
Mathematics, 2022 In this paper, we deal with the general fractional integrals and the general fractional derivatives of arbitrary order with the kernels from a class of functions that have an integrable singularity of power function type at the origin.
Maryam Al-Kandari +2 more
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On the 1st-Level General Fractional Derivatives of Arbitrary Order
Fractal and Fractional, 2023 In this paper, the 1st-level general fractional derivatives of arbitrary order are defined and investigated for the first time. We start with a generalization of the Sonin condition for the kernels of the general fractional integrals and derivatives and ...
Yuri Luchko
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On the Theory of Fractional Calculus in the Pettis-Function Spaces
Journal of Function Spaces, 2018 Throughout this paper, we outline some aspects of fractional calculus in Banach spaces. Some examples are demonstrated. In our investigations, the integrals and the derivatives are understood as Pettis integrals and the corresponding derivatives.
Hussein A. H. Salem
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New Approaches to Fractal–Fractional Bullen’s Inequalities Through Generalized Convexity
Fractal and FractionalThis paper introduces a new identity involving fractal–fractional integrals, which allow us to derive several new Bullen-type inequalities via generalized convexity.
Wedad Saleh +4 more
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On a new class of Hardy-type inequalities with fractional integrals and fractional derivatives [PDF]
, 2014 This paper is devoted to a new class of general weighted Hardy-type inequalities for arbitrary convex functions with some applications to different type of fractional integrals and fractional ...
Krulić Himmelreich, Kristina +2 more
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MathematicsAn initial value problem for a scalar nonlinear differential equation with a variable order for the generalized proportional Caputo fractional derivative is studied. We consider the case of a piecewise constant variable order of the fractional derivative.
Donal O’Regan +3 more
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Riesz potential operators and inverses via fractional centred derivatives
International Journal of Mathematics and Mathematical Sciences, 2006 Fractional centred differences and derivatives definitions are proposed, generalizing to real orders the existing ones valid for even and odd positive integer orders. For each one, suitable integral formulations are obtained.
Manuel Duarte Ortigueira
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