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2015 | 13 | 1 |
Tytuł artykułu

Upper and lower bounds of integral operator defined by the fractional hypergeometric function

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Języki publikacji
EN
Abstrakty
EN
In this article, we impose some studies with applications for generalized integral operators for normalized holomorphic functions. By using the further extension of the extended Gauss hypergeometric functions, new subclasses of analytic functions containing extended Noor integral operator are introduced. Some characteristics of these functions are imposed, involving coefficient bounds and distortion theorems. Further, sufficient conditions for subordination and superordination are illustrated.
Wydawca
Czasopismo
Rocznik
Tom
13
Numer
1
Opis fizyczny
Daty
otrzymano
2015-07-29
zaakceptowano
2015-09-10
online
2015-11-04
Twórcy
  • of Computer Science and Information Technology, University Malaya,
    50603 Kuala Lumpur, Malaysia
  • Institute of Engineering Mathematics, Universiti Malaysia Perlis, 02600 Arau, Malaysia
  • Institute of Engineering Mathematics, Universiti Malaysia Perlis, 02600 Arau, Malaysia
Bibliografia
  • [1] Mandelbrot B.B., Van Ness J.W., Fractional Brownian motions, fractional noises and applications, SIAM review, 1968, 10,422-437.
  • [2] Arovas D., Schrieffer J.R., Wilczek F., Fractional statistics and the quantum Hall effect, Physical review letters, 1984, 53, 722.
  • [3] Wilczek F., Quantum mechanics of fractional-spin particles, Physical review letters, 1982, 49, 957.
  • [4] Baillie R.T., Long memory processes and fractional integration in econometrics, Journal of Econometrics, 1996, 73, 5-59.
  • [5] He J.-H., Approximate analytical solution for seepage flow with fractional derivatives in porous media, Computer Methods inApplied Mechanics and Engineering, 1998, 167 57-68.
  • [6] Hilfer R., et al., Applications of fractional calculus in physics, World Scientific, 2000.[WoS]
  • [7] Baleanu D.,et al., Fractional Calculus: Models and Numerical Methods, World Scientific, 2012
  • [8] Yang X.-J., Advanced local fractional calculus and its applications, World Science, New York, NY, USA, 2012.
  • [9] Wu G.-C., Baleanu D., Discrete fractional logistic map and its chaos, Nonlinear Dynamics, 2014, 75, 283-287.[WoS]
  • [10] Chen F.L., A review of existence and stability results for discrete fractional equations, Journal of Computational Complexity andApplications, 2015, 1, 22-53.
  • [11] Li M., Fractal time series- a tutorial review, Mathematical Problems in Engineering, 2010, 2010 1-26.
  • [12] Yang X. J.,et al., Fractal boundary value problems for integral and differential equations with local fractional operators, ThermalScience, 2015, DOI: 0354-98361300103Y.[WoS]
  • [13] Atici F., Eloe P., Initial value problems in discrete fractional calculus, Proceedings of the American Mathematical Society, 2009,137, 981-989
  • [14] Yang X.-J., Local Fractional Functional Analysis & Its Applications, Asian Academic Publisher Limited Hong Kong, 2011
  • [15] Ibrahim R.W., On generalized Hyers-Ulam stability of admissible functions, Abstract and Applied Analysis, 2012, 2012, 1-10.[WoS]
  • [16] Ibrahim R.W., Modified fractional Cauchy problem in a complex domain, Advances in Difference Equations, 2013, 2013, 1-10.
  • [17] Ibrahim R.W., Jahangiri J., Boundary fractional differential equation in a complex domain, Boundary Value Problems 2014, 2014,1-11.
  • [18] Ibrahim R.W., Sokol J., On a new class of analytic function derived by fractional differential operator, Acta Mathematica Scientia,2014, 34B(4), 1-10.[Crossref][WoS]
  • [19] Ibrahim R.W., Fractional Cauchy problem in sense of the complex Hadamard operators, Mathematics Without Boundaries,Springer, 2014, 259-272.
  • [20] Ibrahim R.W., Studies on generalized fractional operators in complex domain, Mathematics Without Boundaries, Springer, 2014,273-284.
  • [21] Branges L., A proof of the Bieberbach conjecture, Acta Math., 1985, 154, 137–152.[WoS]
  • [22] Srivastava H. M., et al., Generating functions for the generalized Gauss hypergeometric functions, Appl. Math. Comput., 2014,247, 348–352.[WoS]
  • [23] Luo M. J., et al., Some results on the extended beta and extended hypergeometric functions, Appl. Math. Comput., 2014, 248,631–651.[WoS]
  • [24] Srivastava H. M., Choi J., Zeta and q-Zeta Functions and Associated Series and Integrals, Elsevier Science Publishers,Amsterdam, London and New York. 2012.
  • [25] Agarwal P., et al., Extended Riemann-Liouville fractional derivative operator and its applications, J. Nonlinear Sci. Appl., 2015, 8,451–466.
  • [26] S. Ruscheweyh, New criteria for univalent functions, Proceedings of the American Mathematical Society, 1975, 49, 109–115.[WoS]
  • [27] Noor K. L., On new classes of integral operators, Journal of Natural Geometry, 1999, 16, 71–80.
  • [28] Noor K. L., Integral operators defined by convolution with hypergeometric functions, Appl. Math. Comput., 2006, 182, 1872–1881.
  • [29] Ibrahim R. W., Darus M., New classes of analytic functions involving generalized Noor integral operator, Journal of Inequalitiesand Applications, 2008, 390435, 1–14.
  • [30] Miller S. S., Mocanu P. T., Differential Subordinations, Theory and applications, Monographs and Textbooks in Pure and AppliedMathematics, 225, Dekker, New York, 2000.
  • [31] Miller S. S., Mocanu P. T., Subordinants of differetial superordinations, Complex Var. Theory Appl., 2003, 48 (10), 815–826.
  • [32] Brickman L., like analytic functions, Bulletin of the American Mathematical Society, 1973, 79 (3), 555–558.[Crossref]
  • [33] Ruscheweyh St., A subordination theorem for like functions, J. London Math. Soc., 1976, 2(13), 275–280.[Crossref]
  • [34] Bulboaca T., Classes of first-order differential superordinations, Demonstratio Mathematica, 2002, 35(2), 287–292.
  • [35] Ravichandran V., Jayamala M., On sufficient conditions for Caratheodory functions, Far East Journal of Mathematical Sciences,2004, 12, 191–201.
  • [36] Ali R., et al., Differential sandwich theorems for certain analytic functions, Far East Journal of Mathematical Sciences, 2005, 15,87–94.
  • [37] Ibrahim R. W., et al., Third-order differential subordination and superordination involving a fractional operator, Open Mathematics,2015, To appear.
  • [38] Yang X. -J., et al., Local Fractional Integral Transforms and Their Applications, Elsevier, 2015.
  • [39] Yang X. J., Srivastava H. M., Cattani C., Local fractional homotopy perturbation method for solving fractal partial differentialequations arising in mathematical physics, Romanian Reports in Physics, 2015, 67(3), 752-761.
  • [40] Yang X. J., Machado J. T., Hristov J., Nonlinear dynamics for local fractional Burgers’ equation arising in fractal flow. NonlinearDynamics, 2015, 1-5.
  • [41] Yang X. J., Srivastava H. M., An asymptotic perturbation solution for a linear oscillator of free damped vibrations in fractal mediumdescribed by local fractional derivatives. Communications in Nonlinear Science and Numerical Simulation, (2015), 29(1), 499-504.[WoS]
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1515_math-2015-0071
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