Weighted Generalized Fractional Integration by Parts and the Euler–Lagrange Equation [PDF]
Axioms, 2022 Integration by parts plays a crucial role in mathematical analysis, e.g., during the proof of necessary optimality conditions in the calculus of variations and optimal control.
Houssine Zine +3 more
doaj +7 more sources
Fractional operators with boundary points dependent kernels and integration by parts
Discrete and Continuous Dynamical Systems - Series S, 2020 Recently, U. N. Katugampola presented some generalized fractional integrals and derivatives by iterating a \begin{document}$ t^{\rho-1}- $\end{document} weighted integral, \begin{document}$ \rho>0 $\end{document} .
Thabet Abdeljawad
exaly +5 more sources
Mellin transform analysis and integration by parts for Hadamard-type fractional integrals
Journal of Mathematical Analysis and Applications, 2002 The authors consider the known construction of Hadamard fractional integration \[ \mathcal{I}^\alpha_{0+,\mu} f(x)= \frac{1}{\Gamma(\alpha)}\int_0^x\left(\frac{u}{x}\right) ^\mu \left(ln \frac{x}{u}\right)^{ \alpha -1}\frac{f(u) du}{u} \] and some of their modifications. These constructions are invariant with respect to dilations and are related to the
Juan J Trujillo +2 more
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Fractional Hardy–Rellich inequalities via integration by parts
Nonlinear Analysis: Theory, Methods & ApplicationsWe prove a fractional Hardy-Rellich inequality with an explicit constant in bounded domains of class $C^{1,1}$. The strategy of the proof generalizes an approach pioneered by E. Mitidieri (Mat. Zametki, 2000) by relying on a Pohozaev-type identity.
Nicola De Nitti
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Integration by parts for nonsymmetric fractional-order operators on a halfspace [PDF]
Journal of Mathematical Analysis and Applications, 2020 For a strongly elliptic pseudodifferential operator L of order 2a ( 0 a 1 ) with real kernel, we show an integration-by-parts formula for solutions of the homogeneous Dirichlet problem, in the model case where the operator is x-independent with ...
G. Grubb
semanticscholar +6 more sources
Integration by parts and Pohozaev identities for space-dependent fractional-order operators [PDF]
Journal of Differential Equations, 2015 Consider a classical elliptic pseudodifferential operator P on R n of order 2a ( 0 a 1 ) with even symbol. For example, P = A ( x , D ) a where A ( x , D ) is a second-order strongly elliptic differential operator; the fractional Laplacian ( − Δ ) a is a
G. Grubb
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A fractional fundamental lemma and a fractional integration by parts formula -- Applications to critical points of Bolza functionals and to linear boundary value problems [PDF]
Advances in Differential Equations, 2014 In the first part of the paper, we prove a fractional fundamental (du Bois-Reymond) lemma and a fractional variant of the integration by parts formula. The proof of the second result is based on an integral representation of functions possessing Riemann ...
L. Bourdin, D. Idczak
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AppliedMathThis paper investigates a unique and stable numerical approximation of the Riemann–Liouville Fractional Derivative. We utilize diagonal norm finite difference-based time integration methods within the summation-by-parts framework.
Sam Motsoka Rametse +1 more
doaj +2 more sources
Feynman diagrams and a combination of the integration by parts and the integration by fractional expansion techniques [PDF]
Physical Review D, 2010 25 pages, 49 figures, 1 table (typos corrected)
Marcelo Loewe
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Integration by Parts Formula and Applications for SDEs Driven by Fractional Brownian Motions
Stochastic Analysis and Applications, 2012 By using coupling by change of measures, the Driver-type integration by parts formula is established for a class of stochastic differential equations driven by fractional Brownian motions.
Xiliang Fan
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