Search

Your search keyword '"Fractional power"' showing total 596 results
Start Over Descriptor "Fractional power"
596 results on '"Fractional power"'

1. Asymptotic and non-asymptotic results for a binary additive problem involving Piatetski-Shapiro numbers.

Author

Yoshida, Yuuya

Subjects
*FRACTIONAL powers, *EXPONENTIAL sums, *GAMMA functions, *INTEGERS, *COUNTING
Abstract

For all α 1 , α 2 ∈ (1 , 2) with 1 / α 1 + 1 / α 2 > 5 / 3 , we show that the number of pairs (n 1 , n 2) of positive integers with N = ⌊ n 1 α 1 ⌋ + ⌊ n 2 α 2 ⌋ is equal to Γ (1 + 1 / α 1) Γ (1 + 1 / α 2) Γ (1 / α 1 + 1 / α 2) − 1 N 1 / α 1 + 1 / α 2 − 1 + o (N 1 / α 1 + 1 / α 2 − 1) as N → ∞ , where Γ denotes the gamma function. Moreover, we show a non-asymptotic result for the same counting problem when α 1 , α 2 ∈ (1 , 2) lie in a larger range than the above. Finally, we give some asymptotic formulas for similar counting problems in a heuristic way. [ABSTRACT FROM AUTHOR]

Published
2024
Full Text
View/download PDF

2. ON THE SYMBOL CALCULUS FOR MULTIDIMENSIONAL HAUSDORFF OPERATORS.

Author

Liflyand, E. and Mirotin, A.

Subjects
*CALCULUS, *FRACTIONAL powers, *SIGNS & symbols, *HOLOMORPHIC functions, *COMMUTATIVE algebra
Abstract

The aim of this work is to derive a symbol calculus on L 2 (R n) for multidimensional Hausdorff operators. Two aspects of this activity result in two almost independent parts. While throughout the perturbation matrices are supposed to be self-adjoint and form a commuting family, in the second part they are additionally assumed to be positive definite. What relates these two parts is the powerful method of diagonalization of a normal Hausdorff operator elaborated earlier by the second named author. [ABSTRACT FROM AUTHOR]

Published
2024
Full Text
View/download PDF

3. A Higher-Order Non-autonomous Semilinear Parabolic Equation.

Author

Belluzi, Maykel, Bezerra, Flank D. M., Nascimento, Marcelo J. D., and Santos, Lucas A.

Abstract

In this paper, we study results of well-posedness and regularity of higher order in time abstract non-autonomous semilinear Cauchy problems associated with Newton’s binomial theorem and the theory of sectorial operators. Our approach to parabolic problems of arbitrarily order n apparently has never been addressed earlier in the existing literature. Also, we present applications to evolutionary equations involving the fractional Laplacian in bounded smooth domains of R N . [ABSTRACT FROM AUTHOR]

Published
2024
Full Text
View/download PDF

5. On the Study of Pseudo -Asymptotically Periodic Mild Solutions for a Class of Neutral Fractional Delayed Evolution Equations.

Author

Chegloufa, Naceur, Chaouchi, Belkacem, Kostić, Marko, and Du, Wei-Shih

Subjects
*EVOLUTION equations, *FRACTIONAL powers, *GENETIC drift, *LINEAR operators, *PERIODIC functions
Abstract

The goal of this paper is to investigate the existence and uniqueness of pseudo S -asymptotically periodic mild solutions for a class of neutral fractional evolution equations with finite delay. We essentially use the fractional powers of closed linear operators, the semigroup theory and some classical fixed point theorems. Furthermore, we provide an example to illustrate the applications of our abstract results. [ABSTRACT FROM AUTHOR]

Published
2023
Full Text
View/download PDF

6. Approximate controllability results in α-norm for some partial functional integrodifferential equations with nonlocal initial conditions in Banach spaces.

Author

Ndambomve, Patrice, Kpoumie, Moussa El-Khalil, and Ezzinbi, Khalil

Subjects
*INTEGRO-differential equations, *FUNCTIONAL equations, *BANACH spaces, *FRACTIONAL powers, *INTEGRAL operators, *NONLINEAR operators, *CARLEMAN theorem
Abstract

In this work, we discuss the approximate controllability of some nonlinear partial functional integrodifferential equations with nonlocal initial condition in Hilbert spaces. We assume that the corresponding linear part is approximately controllable. The results are obtained by using fractional power theory and α-norm, the measure of noncompactness and the Mönch fixed-point theorem, and the theory of analytic resolvent operators for integral equations. As a result, we obtain a generalization of the work of Mahmudov [N. I. Mahmudov, Approximate controllability of evolution systems with nonlocal conditions, Nonlinear Anal. 68 2008, 3, 536–546], without assuming the compactness of the resolvent operator. Our results extend and complement many other important results in the literature. Finally, a concrete example is given to illustrate the application of the main results. [ABSTRACT FROM AUTHOR]

Published
2023
Full Text
View/download PDF

7. On Fractional Powers of the Schrödinger Operator with a Potential Singular on Manifolds.

Author

Alikulov, T. N. and Khalmukhamedov, A. R.

Abstract

In this paper, the sufficient conditions on summability degree p are found under which the Schrödinger operator with a potential, being singular on manifolds, is a positive one in Banach spaces Lp. It is also demonstrated that the domains of various degrees on this operator form an interpolation pair. In addition to this, the sufficient conditions on p are established which ensure that fractional powers σ, 0 < σ < 1, of this operator are bounded from to Lp. [ABSTRACT FROM AUTHOR]

Published
2023
Full Text
View/download PDF

8. On the Study of Pseudo 𝒮-Asymptotically Periodic Mild Solutions for a Class of Neutral Fractional Delayed Evolution Equations

Author

Naceur Chegloufa, Belkacem Chaouchi, Marko Kostić, and Wei-Shih Du

Subjects
pseudo ?-asymptotically periodic function, neutral fractional evolution equation, mild solution, fractional power, Mathematics, QA1-939
Abstract

The goal of this paper is to investigate the existence and uniqueness of pseudo S-asymptotically periodic mild solutions for a class of neutral fractional evolution equations with finite delay. We essentially use the fractional powers of closed linear operators, the semigroup theory and some classical fixed point theorems. Furthermore, we provide an example to illustrate the applications of our abstract results.

Published
2023
Full Text
View/download PDF

10. Analytical solution of the generalized space-time fractional ultra-hyperbolic differential equation.

Author

Dorrego, Gustavo A.

Subjects
*FRACTIONAL differential equations, *ANALYTICAL solutions, *SPACETIME, *FRACTIONAL powers, *PROBLEM solving, *WAVE equation
Abstract

A generalization of the ultra-hyperbolic time-fractional diffusion-wave equation introduced by the author in Dorrego [The Mittag–Leffler function and its application to the ultra-hyperbolic time-fractional diffusion-wave equation. Integral Transforms Spec. Funct. 2016;27(5):392–404] is presented and studied. The results obtained here extend the previous to the whole space R n . The problem is solved by applying the integral transforms method and the analytical solution is given by the Fox H-function. Some interesting particular cases are analysed. [ABSTRACT FROM AUTHOR]

Published
2022
Full Text
View/download PDF

11. Regularization of a class of ill-posed Cauchy problems associated with generators of analytic semigroups.

Author

Imad, Rezzoug, Taki-Eddine, Oussaeif, and Abdelouahabe, Benbrahim

Subjects
FRACTIONAL powers, BANACH spaces
Abstract

This work is concerned the study of a class of ill-posed Cauchy problems associated with a densely defined linear operatorΑ in a Banach space Ε. It is proved that if - A is the generator of an analytic semigroup, then there exists a family of regularizing operators by using the quasi-reversibility method, fractional powers and semigroups of linear operators. [ABSTRACT FROM AUTHOR]

Published
2022

12. L²-primitive process for retarded stochastic neutral functional differential equations in Hilbert spaces.

Author

Yong Han Kang, Jin-Mun Jeong, and Seong Ho Cho

Subjects
*NONLINEAR functional analysis, *FUNCTIONAL differential equations, *HILBERT space, *LINEAR differential equations, *STOCHASTIC processes, *EXISTENCE theorems, *FRACTIONAL powers
Abstract

In this paper, we study the existence of solutions and L²-primitive process for retarded stochastic neutral functional differential equations in Hilbert spaces. We no longer require the Azera-Ascoli theorem to prove the existence of continuous solutions of nonlinear differential systems, but instead we apply the regularity results of general linear differential equations to the case the L²-primitive process for retarded stochastic neutral functional differential systems with unbounded principal operators, delay terms and local Lipschitz continuity of the nonlinear term. Finally, we give a simple example to which our main result can be applied. [ABSTRACT FROM AUTHOR]

Published
2021

13. A Singularly Perturbed Boundary Value Problems with Fractional Powers of Elliptic Operators

Author

Vabishchevich, Petr N., Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Weikum, Gerhard, Series editor, Dimov, Ivan, editor, Faragó, István, editor, and Vulkov, Lubin, editor

Published
2017
Full Text
View/download PDF

14. Fractional approximations of abstract semilinear parabolic problems.

Author

Bezerra, Flank D. M., Carvalho, Alexandre N., and Nascimento, Marcelo J. D.

Subjects
WAVE equation, BANACH spaces, FRACTIONAL powers, PARABOLIC operators, CONTINUITY
Abstract

In this paper we study the abstract semilinear parabolic problem of the form du/dt + Au = ƒ(u), as the limit of the corresponding fractional approximations du/dt + Aαu = ƒ(u), in a Banach space X, where the operator A : D(A) ⊂ X → X is a sectorial operator in the sense of Henry [22]. Under suitable assumptions on nonlinearities ƒ : Xα → X (Xα : = D(Aα)), we prove the continuity with rate (with respect to the parameter α) for the global attractors (as seen in Babin and Vishik [4] Chapter 8, Theorem 2.1). As an application of our analysis we consider a fractional approximation of the strongly damped wave equations and we study the convergence with rate of solutions of such approximations. [ABSTRACT FROM AUTHOR]

Published
2020
Full Text
View/download PDF

17. Rockland operators and Sobolev spaces

Author

Fischer, Veronique, Ruzhansky, Michael, Bass, Hyman, Series editor, Lu, Jiang-Hua, Series editor, Oesterlé, Joseph, Series editor, Tschinkel, Yuri, Series editor, Fischer, Veronique, and Ruzhansky, Michael

Published
2016
Full Text
View/download PDF

18. Operator Theory and Semigroups

Author

Prüss, Jan, Simonett, Gieri, Amann, Herbert, Series editor, Bourguignon, Jean Pierre, Series editor, Chen, William Y.C., Series editor, Grove, Karsten, Series editor, Vasiliev, Alexander, Series editor, Prüss, Jan, and Simonett, Gieri

Published
2016
Full Text
View/download PDF

21. A remark on the H ∞-calculus

Author

Gesztesy, Fritz, Godefroy, Gilles, Grafakos, Loukas, Verbitsky, Igor, Kung, Joseph P. S., Series editor, Gesztesy, Fritz, editor, Godefroy, Gilles, editor, Grafakos, Loukas, editor, and Verbitsky, Igor, editor

Published
2016
Full Text
View/download PDF

22. Norm estimates for functions of non-selfadjoint operators nonregular on the convex hull of the spectrum

Author

Gil’ Michael

Subjects
functions of non-selfadjoint operators, logarithm, fractional power, meromorphic function, Mathematics, QA1-939
Abstract

We consider a bounded linear operator A in a Hilbert space with a Hilbert-Schmidt Hermitian component (A − A*)/2i. A sharp norm estimate is established for functions of A nonregular on the convex hull of the spectrum. The logarithm, fractional powers and meromorphic functions of operators are examples of such functions. Our results are based on the existence of a sequence An (n = 1, 2, ...) of finite dimensional operators strongly converging to A, whose spectra belongs to the spectrum of A. Besides, it is shown that the resolvents and holomorphic functions of An strongly converge to the resolvent and corresponding function of A.

Published
2017
Full Text
View/download PDF

24. Properties of Solutions

Author

Li, Tatsien, Tan, Yongji, Cai, Zhijie, Chen, Wei, Wang, Jingnong, Alladi, Krishnaswami, Series editor, Bellomo, Nicola, Series editor, Benzi, Michele, Series editor, Li, Tatsien, Series editor, Neufang, Matthias, Series editor, Scherzer, Otmar, Series editor, Schleicher, Dierk, Series editor, Sidoravicius, Vladas, Series editor, Steinberg, Benjamin, Series editor, Tschinkel, Yuri, Series editor, Tu, Loring W., Series editor, Yin, G. George, Series editor, Zhang, Ping, Series editor, Tan, Yongji, Cai, Zhijie, Chen, Wei, and Wang, Jingnong

Published
2014
Full Text
View/download PDF

25. Philosophy and Overview of the Book

Author

Talagrand, Michel, Ambrosio, Luigi, Series editor, Greuel, Gert-Martin, Series editor, Gromov, Misha, Series editor, Jost, Jürgen, Series editor, Kollár, János, Series editor, Kudla, Stephen S., Series editor, Laumon, Gérard, Series editor, Lenstra, Hendrik W., Series editor, Tits, Jacques, Series editor, Zagier, Don B., Series editor, and Talagrand, Michel

Published
2014
Full Text
View/download PDF

26. The Ultimate Matching Theorem in Dimension ≥3

Author

Talagrand, Michel, Ambrosio, Luigi, Series editor, Greuel, Gert-Martin, Series editor, Gromov, Misha, Series editor, Jost, Jürgen, Series editor, Kollár, János, Series editor, Kudla, Stephen S., Series editor, Laumon, Gérard, Series editor, Lenstra, Hendrik W., Series editor, Tits, Jacques, Series editor, Zagier, Don B., Series editor, and Talagrand, Michel

Published
2014
Full Text
View/download PDF

28. Multivalued Elementary Functions in Computer-Algebra Systems

Author

Jeffrey, David J., Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Kobsa, Alfred, Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Nierstrasz, Oscar, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Weikum, Gerhard, Series editor, Goebel, Randy, Series editor, Tanaka, Yuzuru, Series editor, Wahlster, Wolfgang, Series editor, Siekmann, Jörg, Series editor, Aranda-Corral, Gonzalo A., editor, Calmet, Jacques, editor, and Martín-Mateos, Francisco J., editor

Published
2014
Full Text
View/download PDF

32. Comparative analysis of suitability of fractional derivatives in modelling the practical capacitor

Author

Rawid Banchuin

Subjects
Electrolytic capacitor, Work (thermodynamics), Applied Mathematics, Function (mathematics), Transient analysis, Capacitance, Fractional power, Computer Science Applications, law.invention, Fractional calculus, Capacitor, Computational Theory and Mathematics, law, Applied mathematics, Electrical and Electronic Engineering, Mathematics
Abstract

Purpose The purpose of this paper is to compare the suitability of fractional derivatives in the modelling of practical capacitors. Such suitability refers to ability to provide the analytical capacitance function that matches the experimental ones of each fractional derivative. Design/methodology/approach The analytical capacitance functions based on various fractional derivatives of both local and nonlocal types including the author’s have been derived. The derived capacitance functions have been simulated and compared with the experimental ones of aluminium electrolytic and electrical double layer capacitors (EDLCs). Findings This paper has found that any local fractional derivative with fractional power law-based relationship with the conventional one is suitable for modelling the aluminium electrolytic capacitor (AEC) by incorporating with the conventional capacitance definition. On the other hand, the author’s nonlocal fractional derivatives have been found to be more suitable than the others for modelling the EDLC by incorporating with the revisited definition of capacitance. Originality/value The proposed comparative analysis has been originally presented in this work. The criterion for local fractional derivative, to be suitable for modelling the AEC, has been found. The nonlocal fractional operators which are most suitable for modelling the EDLC have been derived where the unsuitable one has been pointed out.

Published
2021
Full Text
View/download PDF

33. A Gaussian Method for the Square Root of Accretive Operators

Author

Eleonora Denich, Paolo Novati, Denich, E., and Novati, P.

Subjects
Fractional power, Fractional powers, Computational Mathematics, Numerical Analysis, regularly accretive operators, Applied Mathematics, Gaussian quadrature rule, regularly accretive operator
Abstract

We consider the approximation of the inverse square root of regularly accretive operators in Hilbert spaces. The approximation is of rational type and comes from the use of the Gauss–Legendre rule applied to a special integral formulation of the fractional power. We derive sharp error estimates, based on the use of the numerical range, and provide some numerical experiments. For practical purposes, the finite-dimensional case is also considered. In this setting, the convergence is shown to be of exponential type. The method is also tested for the computation of a generic fractional power.

Published
2023
Full Text
View/download PDF

35. Existence and uniqueness of mild solutions for fractional semilinear differential equations

Author

Bambang Hendriya Guswanto and Takashi Suzuki

Subjects
Fractional semilinear differential equation, sectorial operator, Caputo fractional derivative, fractional power, mild solution, Mathematics, QA1-939
Abstract

In this article, we study the existence and uniqueness of a local mild solution for a class of semilinear differential equations involving the Caputo fractional time derivative of order $\alpha$ $(0

Published
2015

39. Growth of Power-Free Languages over Large Alphabets

Author

Shur, Arseny M., Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Doug, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Ablayev, Farid, editor, and Mayr, Ernst W., editor

Published
2010
Full Text
View/download PDF

43. Semigroups of Operators and Interpolation

Author

Başar, Tamer, editor, Åström, Karl Johan, editor, Chen, Han-Fu, editor, Helton, William, editor, Isidori, Alberto, editor, Kokotović, Petar V., editor, Kurzhanski, Alexander, editor, Poor, H. Vincent, editor, Soner, Mete, editor, Bensoussan, Alain, Da Prato, Giuseppe, Delfour, Michel C., and Mitter, Sanjoy K.

Published
2007
Full Text
View/download PDF

44. Kolmogorov Complexity, Lovász Local Lemma and Critical Exponents

Author

Rumyantsev, Andrey Yu., Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Doug, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Diekert, Volker, editor, Volkov, Mikhail V., editor, and Voronkov, Andrei, editor

Published
2007
Full Text
View/download PDF

45. Anisotropic α-Kernels and Associated Flows

Author

Feigin, Micha, Sochen, Nir, Vemuri, Baba C., Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Rangan, C. Pandu, editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Doug, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Sgallari, Fiorella, editor, Murli, Almerico, editor, and Paragios, Nikos, editor

Published
2007
Full Text
View/download PDF

46. Fractional Powers and Semigroups

Author

Haase, Markus, Gohberg, I., editor, Alpay, D., editor, Arazy, J., editor, Atzmon, A., editor, Ball, J. A., editor, Ben-Artzi, A., editor, Bercovici, H., editor, Böttcher, A., editor, Clancey, K., editor, Coburn, L. A., editor, Curto, R. E., editor, Davidson, K. R., editor, Douglas, R. G., editor, Dijksma, A., editor, Dym, H., editor, Fuhrmann, P. A., editor, Gramsch, B., editor, Helton, J. A., editor, Kaashoek, M. A., editor, Kaper, H. G., editor, Kuroda, S. T., editor, Lancaster, P., editor, Lerer, L. E., editor, Mityagin, B., editor, Olshevsky, V., editor, Putinar, M., editor, Rodman, L., editor, Rovnyak, J., editor, Sarason, D. E., editor, Spitkovsky, I. M., editor, Treil, S., editor, Upmeier, H., editor, Verduyn Lunel, S. M., editor, Voiculescu, D., editor, Xia, D., editor, Yafaev, D., editor, and Haase, Markus

Published
2006
Full Text
View/download PDF

47. Regularity and Scale-Space Properties of Fractional High Order Linear Filtering

Author

Didas, Stephan, Burgeth, Bernhard, Imiya, Atsushi, Weickert, Joachim, Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Dough, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Kimmel, Ron, editor, Sochen, Nir A., editor, and Weickert, Joachim, editor

Published
2005
Full Text
View/download PDF

49. On the fractional Bessel operator

Author

M. Garayev and F. Bouzeffour

Subjects
symbols.namesake, Diffusion equation, Applied Mathematics, Operator (physics), Mathematical analysis, symbols, Canonical form, Analysis, Bessel function, Fractional power, Mathematics, Fractional calculus
Abstract

In this paper, we investigate the fractional power (−Δν)γ/2, 0 −1/2. Our method uses a canonical representation for generalized Laplacia...

Published
2021
Full Text
View/download PDF

50. Semigroup Methods

Author

Marsden, J. E., editor, Antman, S. S., editor, Sirovich, L., editor, Renardy, Michael, and Rogers, Robert C.

Published
2004
Full Text
View/download PDF

Catalog

Books, media, physical & digital resources
See catalog results