Results 211 to 220 of about 10,319 (253)
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Fractional integration by parts and Sobolev‐type inequalities for ψ$$ \psi $$‐fractional operators
Mathematical Methods in the Applied Sciences, 2022In the present paper, we investigate the Hardy–Littlewood type and the integration by parts result for ψ$$ \psi $$ –Riemann–Liouville fractional integrals.
Cesar E Torres Ledesma, JOSÉ Sousa
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An Integration by Parts Formula for Stochastic Heat Equations with Fractional Noise
Acta Mathematica Scientia, 2022zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yin Xiuwei
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On Fractional Integration by Parts
Proceedings of the London Mathematical Society, 1938Let \((a,b)\) be a finite interval, \(f\in L(a,b)\), \(\alpha>0\), \[ f_\alpha^+\equiv f_\alpha^+(a,x) = (\Gamma(\alpha))^{-1} \int_a^x f(t)(x-t)^{\alpha-1}\,dt, \; f_\alpha^-\equiv f_\alpha^-(a,x) = (\Gamma(\alpha))^{-1} \int_x^b f(t)(t-x)^{\alpha-1}\,dt. \] As a consequence of results of Hardy and Littlewood the authors prove that if \(p>1\), \(q>1\),
E. Love, L. Young
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On a more general fractional integration by parts formulae and applications
Physica A: Statistical Mechanics and Its Applications, 2019The integration by part comes from the product rule of classical differentiation and integration. The concept was adapted in fractional differential and integration and has several applications in control theory.
J F Gómez-Aguilar +2 more
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On integration by parts formula and characterization of fractional Ornstein–Uhlenbeck process
Statistics and Probability Letters, 2015zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xiaoxia Sun, Feng Guo
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Integration by Parts Formula for Regional Fractional Laplacian
Communications in Mathematical Physics, 2006The generator of a symmetric \(\alpha\)-stable process is the fractional Laplacian \(-(-\Delta)^{\alpha/2}\). As this operator is non-local, it cannot be restricted to a domain automatically. Restricting the corresponding integral kernel leads to a jump-process on a domain \(G\) -- called censored stable process. The corresponding generator \(\Delta_G^{
Qingyang Guan
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Georgian Mathematical Journal, 2019
In the paper, we derive a formula of integration by parts for the left-sided Hilfer derivative. Moreover, we present a formula of such a type for the right-sided Hilfer derivative. These results generalize the well-known rules of integration by parts for
R. Kamocki
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In the paper, we derive a formula of integration by parts for the left-sided Hilfer derivative. Moreover, we present a formula of such a type for the right-sided Hilfer derivative. These results generalize the well-known rules of integration by parts for
R. Kamocki
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TRANSFORMATION OF HYPERGEOMETRIC INTEGRALS BY MEANS OF FRACTIONAL INTEGRATION BY PARTS
The Quarterly Journal of Mathematics, 1939A. Erdélyi
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Journal of Vibration and Control, 2021
The treatment of fractional differential equations and fractional optimal control problems is more difficult to tackle than the standard integer-order counterpart and may pose problems to non-specialists.
A. Hendy +2 more
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The treatment of fractional differential equations and fractional optimal control problems is more difficult to tackle than the standard integer-order counterpart and may pose problems to non-specialists.
A. Hendy +2 more
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Evaluation of fractional order of the discrete integrator. Part II
Fractional Calculus and Applied Analysis, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ostalczyk, Piotr +3 more
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