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Journal articles on the topic 'Association of fractional operators'

Author: Grafiati

Published: 4 June 2021

Last updated: 7 February 2022

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1

Ahmad, Shabir, Aman Ullah, Ali Akgül, and Manuel De la Sen. "Study of HIV Disease and Its Association with Immune Cells under Nonsingular and Nonlocal Fractal-Fractional Operator." Complexity 2021 (August 19, 2021): 1–12. http://dx.doi.org/10.1155/2021/1904067.

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HIV, like many other infections, is a severe and lethal infection. Fractal-fractional operators are frequently used in modeling numerous physical processes in the current decade. These operators provide better dynamics of a mathematical model because these are the generalization of integer and fractional-order operators. This paper aims to study the dynamics of the HIV model during primary infection by fractal-fractional Atangana–Baleanu (AB) operators. The sufficient conditions for the existence and uniqueness of the solution of the proposed model under the AB operator are derived via fixed p

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2

Petrosyan, Garik G. "On adjoint operators for fractional differentiation operators." Russian Universities Reports. Mathematics, no. 131 (2020): 284–89. http://dx.doi.org/10.20310/2686-9667-2020-25-131-284-289.

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On a linear manifold of the space of square summable functions on a finite segment vanishing at its ends, we consider the operator of left-sided Caputo fractional differentiation. We prove that the adjoint for it is the operator of right-sided Caputo fractional differentiation. Similar results are established for the Riemann–Liouville fractional differentiation operators. We also demonstrate that the operator, which is represented as the sum of the left-sided and the right-sided fractional differentiation operators is self adjoint. The known properties of the Caputo and Riemann–Liouville fract

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3

Case, Jeffrey S., and Sun-Yung Alice Chang. "On Fractional GJMS Operators." Communications on Pure and Applied Mathematics 69, no. 6 (2015): 1017–61. http://dx.doi.org/10.1002/cpa.21564.

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4

MARTINEZ, Celso, Miguel SANZ, and Luis MARCO. "Fractional powers of operators." Journal of the Mathematical Society of Japan 40, no. 2 (1988): 331–47. http://dx.doi.org/10.2969/jmsj/04020331.

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5

Fan, Da Shan, and Fa You Zhao. "Multilinear fractional Hausdorff operators." Acta Mathematica Sinica, English Series 30, no. 8 (2014): 1407–21. http://dx.doi.org/10.1007/s10114-014-3552-2.

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6

Khan, Tahir Ullah, and Muhammad Adil Khan. "Generalized conformable fractional operators." Journal of Computational and Applied Mathematics 346 (January 2019): 378–89. http://dx.doi.org/10.1016/j.cam.2018.07.018.

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7

Schiavone, S. E. "Fractional powers of operators and Riesz fractional integrals." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 112, no. 3-4 (1989): 237–47. http://dx.doi.org/10.1017/s0308210500018709.

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SynopsisIn this paper, a theory of fractional powers of operators due to Balakrishnan, which is valid for certain operators on Banach spaces, is extended to Fréchet spaces. The resultingtheory is shown to be more general than that developed in an earlier approach by Lamb, and is applied to obtain mapping properties of certain Riesz fractional integral operators on spaces of test functions.

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8

Atici, Ferhan, and Meltem Uyanik. "Analysis of discrete fractional operators." Applicable Analysis and Discrete Mathematics 9, no. 1 (2015): 139–49. http://dx.doi.org/10.2298/aadm150218007a.

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In this paper, we introduce two new monotonicity concepts for a nonnegative or nonpositive valued function defined on a discrete domain. We give examples to illustrate connections between these new monotonicity concepts and the traditional ones. We then prove some monotonicity criteria based on the sign of the fractional difference operator of a function f, ??f with 0 < ? < 1. As an application, we state and prove the mean value theorem on discrete fractional calculus.

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9

Ansari, Alireza, Mohammadreza Ahmadi Darani, and Mohammad Moradi. "On Fractional Mittag–Leffler Operators." Reports on Mathematical Physics 70, no. 1 (2012): 119–31. http://dx.doi.org/10.1016/s0034-4877(13)60017-8.

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10

Grumiau, C., M. Squassina, and C. Troestler. "Asymptotic symmetries for fractional operators." Nonlinear Analysis: Real World Applications 26 (December 2015): 351–71. http://dx.doi.org/10.1016/j.nonrwa.2015.06.001.

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11

TANAKA, HITOSHI. "MORREY SPACES AND FRACTIONAL OPERATORS." Journal of the Australian Mathematical Society 88, no. 2 (2010): 247–59. http://dx.doi.org/10.1017/s1446788709000457.

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AbstractThe relation between the fractional integral operator and the fractional maximal operator is investigated in the framework of Morrey spaces. Applications to the Fefferman–Phong and the Olsen inequalities are also included.

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12

Tuan, Vu Kim, and Megumi Saigo. "Multidimensional Modified Fractional Calculus Operators." Mathematische Nachrichten 161, no. 1 (1993): 253–70. http://dx.doi.org/10.1002/mana.19931610119.

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13

Jain, Rashmi, and M. A. Pathan. "On Weyl fractional integral operators." Tamkang Journal of Mathematics 35, no. 2 (2004): 169–74. http://dx.doi.org/10.5556/j.tkjm.35.2004.218.

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In this paper, we first establish an interesting theorem exhibiting a relationship existing between the Laplace transform and Weyl fractional integral operator of related functions. This theorem is sufficiently general in nature as it contains $n$ series involving arbitrary complex numbers $ \Omega(r_1,\ldots r_n) $. We have obtained here as applications of the theorem, the Weyl fractional integral operators of Kamp'e de F'eriet function, Appell's functions $ F_1 $, $ F_4 $, Humbert's function $ \Psi_1$ and Lauricella's, triple hypergeometric series $ F_E $. References of known results which f

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14

Baeumer, Boris, Mark M. Meerschaert, and Jeff Mortensen. "Space-time fractional derivative operators." Proceedings of the American Mathematical Society 133, no. 8 (2005): 2273–82. http://dx.doi.org/10.1090/s0002-9939-05-07949-9.

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15

Gupta, K. C., and R. C. Soni. "On unified fractional integral operators." Proceedings of the Indian Academy of Sciences - Section A 106, no. 1 (1996): 53–64. http://dx.doi.org/10.1007/bf02837186.

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16

Gaul, L., P. Klein, and S. Kemple. "Damping description involving fractional operators." Mechanical Systems and Signal Processing 5, no. 2 (1991): 81–88. http://dx.doi.org/10.1016/0888-3270(91)90016-x.

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17

Sawano, Yoshihiro, Satoko Sugano, and Hitoshi Tanaka. "Generalized fractional integral operators and fractional maximal operators in the framework of Morrey spaces." Transactions of the American Mathematical Society 363, no. 12 (2011): 6481–503. http://dx.doi.org/10.1090/s0002-9947-2011-05294-3.

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18

Deng, Weihua, Buyang Li, Wenyi Tian, and Pingwen Zhang. "Boundary Problems for the Fractional and Tempered Fractional Operators." Multiscale Modeling & Simulation 16, no. 1 (2018): 125–49. http://dx.doi.org/10.1137/17m1116222.

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19

Xu, Qinwu, and Zhoushun Zheng. "Spectral Collocation Method for Fractional Differential/Integral Equations with Generalized Fractional Operator." International Journal of Differential Equations 2019 (January 1, 2019): 1–14. http://dx.doi.org/10.1155/2019/3734617.

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Generalized fractional operators are generalization of the Riemann-Liouville and Caputo fractional derivatives, which include Erdélyi-Kober and Hadamard operators as their special cases. Due to the complicated form of the kernel and weight function in the convolution, it is even harder to design high order numerical methods for differential equations with generalized fractional operators. In this paper, we first derive analytical formulas for α-th (α>0) order fractional derivative of Jacobi polynomials. Spectral approximation method is proposed for generalized fractional operators through a

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20

Mustard, David. "Fractional convolution." Journal of the Australian Mathematical Society. Series B. Applied Mathematics 40, no. 2 (1998): 257–65. http://dx.doi.org/10.1017/s0334270000012509.

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AbstractA continuous one-parameter set of binary operators on L2(R) called fractional convolution operators and which includes those of multiplication and convolution as particular cases is constructed by means of the Condon-Bargmann fractional Fourier transform. A fractional convolution theorem generalizes the standard Fourier convolution theorems and a fractional unit distribution generalizes the unit and delta distributions. Some explicit double-integral formulas for the fractional convolution between two functions are given and the induced operation between their corresponding Wigner distr

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21

Samraiz, Muhammad, Muhammad Umer, Artion Kashuri, Thabet Abdeljawad, Sajid Iqbal, and Nabil Mlaiki. "On Weighted (k, s)-Riemann-Liouville Fractional Operators and Solution of Fractional Kinetic Equation." Fractal and Fractional 5, no. 3 (2021): 118. http://dx.doi.org/10.3390/fractalfract5030118.

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In this article, we establish the weighted (k,s)-Riemann-Liouville fractional integral and differential operators. Some certain properties of the operators and the weighted generalized Laplace transform of the new operators are part of the paper. The article consists of Chebyshev-type inequalities involving a weighted fractional integral. We propose an integro-differential kinetic equation using the novel fractional operators and find its solution by applying weighted generalized Laplace transforms.

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22

Lanzhe, Liu. "Continuity for some multilinear operators of integral operators on Triebel-Lizorkin spaces." International Journal of Mathematics and Mathematical Sciences 2004, no. 38 (2004): 2039–47. http://dx.doi.org/10.1155/s0161171204303121.

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The continuityfor some multilinear operators related to certain fractional singular integral operators on Triebel-Lizorkin spaces is obtained. The operators include Calderon-Zygmund singular integral operator and fractional integral operator.

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23

Anastassiou, George A. "Vectorial Fractional Approximation by Linear Operators." Progress in Fractional Differentiation and Applications 3, no. 3 (2017): 175–90. http://dx.doi.org/10.18576/pfda/030301.

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24

Baleanu, Dumitru, and Arran Fernandez. "On Fractional Operators and Their Classifications." Mathematics 7, no. 9 (2019): 830. http://dx.doi.org/10.3390/math7090830.

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Fractional calculus dates its inception to a correspondence between Leibniz and L’Hopital in 1695, when Leibniz described “paradoxes” and predicted that “one day useful consequences will be drawn” from them. In today’s world, the study of non-integer orders of differentiation has become a thriving field of research, not only in mathematics but also in other parts of science such as physics, biology, and engineering: many of the “useful consequences” predicted by Leibniz have been discovered. However, the field has grown so far that researchers cannot yet agree on what a “fractional derivative”

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25

Bès, J., Ö. Martin, and A. Peris. "Disjoint hypercyclic linear fractional composition operators." Journal of Mathematical Analysis and Applications 381, no. 2 (2011): 843–56. http://dx.doi.org/10.1016/j.jmaa.2011.03.072.

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26

GUNAWAN, H., Y. SAWANO, and I. SIHWANINGRUM. "FRACTIONAL INTEGRAL OPERATORS IN NONHOMOGENEOUS SPACES." Bulletin of the Australian Mathematical Society 80, no. 2 (2009): 324–34. http://dx.doi.org/10.1017/s0004972709000343.

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AbstractWe discuss here the boundedness of the fractional integral operatorIαand its generalized version on generalized nonhomogeneous Morrey spaces. To prove the boundedness ofIα, we employ the boundedness of the so-called maximal fractional integral operatorIa,κ*. In addition, we prove an Olsen-type inequality, which is analogous to that in the case of homogeneous type.

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27

Galué, Leda, S. L. Kalla, and Vu Kim Tuan. "Composition of erdélyi-kober fractional operators." Integral Transforms and Special Functions 9, no. 3 (2000): 185–96. http://dx.doi.org/10.1080/10652460008819254.

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28

Bourdon, Paul S. "Components of linear-fractional composition operators." Journal of Mathematical Analysis and Applications 279, no. 1 (2003): 228–45. http://dx.doi.org/10.1016/s0022-247x(03)00004-0.

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29

Kokilashvili, Vakhtang, Mieczysław Mastyło, and Alexander Meskhi. "Compactness criteria for fractional integral operators." Fractional Calculus and Applied Analysis 22, no. 5 (2019): 1269–83. http://dx.doi.org/10.1515/fca-2019-0067.

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Abstract We establish necessary and sufficient conditions for the compactness of fractional integral operators from Lp(X, μ) to Lq(X, μ) with 1 < p < q < ∞, where μ is a measure on a quasi-metric measure space X. As an application we obtain criteria for the compactness of fractional integral operators defined in weighted Lebesgue spaces over bounded domains of the Euclidean space ℝn with the Lebesgue measure, and also for the fractional integral operator associated to rectifiable curves of the complex plane.

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30

Bourdon, P. S., E. E. Fry, C. Hammond, and C. H. Spofford. "Norms of linear-fractional composition operators." Transactions of the American Mathematical Society 356, no. 6 (2003): 2459–80. http://dx.doi.org/10.1090/s0002-9947-03-03374-9.

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31

Khan, A. M., R. K. Kumbhat, Amit Chouhan, and Anita Alaria. "Generalized Fractional Integral Operators andM-Series." Journal of Mathematics 2016 (2016): 1–10. http://dx.doi.org/10.1155/2016/2872185.

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Two fractional integral operators associated with FoxH-function due to Saxena and Kumbhat are applied toM-series, which is an extension of both Mittag-Leffler function and generalized hypergeometric functionpFq. The Mellin and Whittaker transforms are obtained for these compositional operators withM-series. Further some interesting properties have been established including power function and Riemann-Liouville fractional integral operators. The results are expressed in terms ofH-function, which are in compact form suitable for numerical computation. Special cases of the results are also pointe

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32

Adams, Jay L., and Tom t. Hartley. "Hankel operators for fractional-order systems." Journal Européen des Systèmes Automatisés 42, no. 6-8 (2008): 701–13. http://dx.doi.org/10.3166/jesa.42.701-713.

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33

Taverna, Giorgio S., and Delfim F. M. Torres. "Generalized fractional operators for nonstandard Lagrangians." Mathematical Methods in the Applied Sciences 38, no. 9 (2014): 1808–12. http://dx.doi.org/10.1002/mma.3188.

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34

Nchama, Gustavo Asumu M. Boro. "Properties of Caputo-Fabrizio fractional operators." New Trends in Mathematical Science 1, no. 8 (2020): 001–25. http://dx.doi.org/10.20852/ntmsci.2020.393.

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35

Auscher, Pascal, and Jose Maria Martell. "Weighted norm inequalities for fractional operators." Indiana University Mathematics Journal 57, no. 4 (2008): 1845–70. http://dx.doi.org/10.1512/iumj.2008.57.3236.

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36

Harir, Atimad, Said Melliani, and Lalla Saadia Chadli. "Fuzzy Conformable Fractional Semigroups of Operators." International Journal of Differential Equations 2020 (November 3, 2020): 1–6. http://dx.doi.org/10.1155/2020/8836011.

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In this paper, we introduce a fuzzy fractional semigroup of operators whose generator will be the fuzzy fractional derivative of the fuzzy semigroup at t = 0 . We establish some of their proprieties and some results about the solution of fuzzy fractional Cauchy problem.

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37

d’Avenia, Pietro, and Marco Squassina. "Ground states for fractional magnetic operators." ESAIM: Control, Optimisation and Calculus of Variations 24, no. 1 (2017): 1–24. http://dx.doi.org/10.1051/cocv/2016071.

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We study a class of minimization problems for a nonlocal operator involving an external magnetic potential. The notions are physically justified and consistent with the case of absence of magnetic fields. Existence of solutions is obtained via concentration compactness.

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38

Babakhani, Azizollah, Milad Yadollahzadeh, and Abdolali Neamaty. "Some properties of pseudo-fractional operators." Journal of Pseudo-Differential Operators and Applications 9, no. 3 (2017): 677–700. http://dx.doi.org/10.1007/s11868-017-0206-z.

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39

Sawano, Yoshihiro, Satoko Sugano, and Hitoshi Tanaka. "Orlicz–Morrey Spaces and Fractional Operators." Potential Analysis 36, no. 4 (2011): 517–56. http://dx.doi.org/10.1007/s11118-011-9239-8.

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40

Agarwal, Ravi P., Asma, Vasile Lupulescu, and Donal O’Regan. "Fractional semilinear equations with causal operators." Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas 111, no. 1 (2016): 257–69. http://dx.doi.org/10.1007/s13398-016-0292-4.

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41

Rivero, Margarita, Luis Rodríguez-Germá, Juan J. Trujillo, and M. Pilar Velasco. "Fractional operators and some special functions." Computers & Mathematics with Applications 59, no. 5 (2010): 1822–34. http://dx.doi.org/10.1016/j.camwa.2009.08.026.

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42

Acuña Valverde, Luis. "Trace asymptotics for fractional Schrödinger operators." Journal of Functional Analysis 266, no. 2 (2014): 514–59. http://dx.doi.org/10.1016/j.jfa.2013.10.021.

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43

Stein, Elias M., and Stephen Wainger. "Two discrete fractional integral operators revisited." Journal d'Analyse Mathématique 87, no. 1 (2002): 451–79. http://dx.doi.org/10.1007/bf02868485.

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44

Eridani, A., Vakhtang Kokilashvili, and Alexander Meskhi. "Morrey spaces and fractional integral operators." Expositiones Mathematicae 27, no. 3 (2009): 227–39. http://dx.doi.org/10.1016/j.exmath.2009.01.001.

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45

Baliarsingh, P., and L. Nayak. "A note on fractional difference operators." Alexandria Engineering Journal 57, no. 2 (2018): 1051–54. http://dx.doi.org/10.1016/j.aej.2017.02.022.

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46

Canqin, Tang, Yang Dachun, and Zhang Pu. "Boundedness of generalized fractional integral operators." Analysis in Theory and Applications 18, no. 4 (2002): 31–47. http://dx.doi.org/10.1007/bf02845273.

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47

Cowen, Carl C. "Linear fractional composition operators on H2." Integral Equations and Operator Theory 11, no. 2 (1988): 151–60. http://dx.doi.org/10.1007/bf01272115.

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48

Gomilko, A. M. "Purely imaginary fractional powers of operators." Functional Analysis and Its Applications 25, no. 2 (1991): 148–50. http://dx.doi.org/10.1007/bf01079601.

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49

Demeter, Ciprian, Malabika Pramanik, and Christoph Thiele. "Multilinear singular operators with fractional rank." Pacific Journal of Mathematics 246, no. 2 (2010): 293–324. http://dx.doi.org/10.2140/pjm.2010.246.293.

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50

Agarwal, Praveen, and Junesang Choi. "CERTAIN FRACTIONAL INTEGRAL INEQUALITIES ASSOCIATED WITH PATHWAY FRACTIONAL INTEGRAL OPERATORS." Bulletin of the Korean Mathematical Society 53, no. 1 (2016): 181–93. http://dx.doi.org/10.4134/bkms.2016.53.1.181.

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