Conference submissions

Ultimate behavior of some stochastic non-linear fractional parabolic systems
Mahmoud El-Borai, Alexandria University Faculty of Science Alexandria Egypt, Mathematics and Computer Sciences, Egypt
Abstract: Ultimate behavior of some stochastic non-linear fractional parabolic systems Mahmoud M.Elborai , Khairia El-said El-Nadi m_m_elborai@yahoo.com, khairia_el_said@hotmail.com Alexandria University- Faculty of Science – Department of Mathematics and Computer Science Abstract Problems of the form; (∂^α u_i (x,t))/(∂t^α )=c L_i u_i (x,t)+c f_i (H(t),u)+ c^2 F_i (S(t),x,u),t>0 ,0< α≤ 1 u_i (x,0)=〖 φ〗_i (x), i = 1,……,n Are considered, where L_1,L_2,…..,L_nare elliptic partial differential operators of higher orders and with coefficients depending onx={x_1,….,x_m } ,-∞
Fractional differential equations with Geogebra (Jorge Olivares , Pablo Martin and Fernando Maass)
Jorge Olivares, Universidad de Antofagasta, Matemáticas, Chile
Abstract: With the arrival of technology in our time, several investigations have been carried out and several mathematical softwares and programs have been developed using computers in the mathematical teaching . The aim of this work is to solve fractional differential equations (df^α (x))/(dx^α )=Ax+B , (A, B constants ) using the mathematical software geogebra [1].The initial condition is f(0)=0 , 0< α<1. Caputo definition for the fractional derivatives is considered [2]. References. [1]. Güven, B. & Kösa, T. “The effect of dynamic geometry software on student mathematics teachers spatial visualization skills”. The Turkish Online Journal of Educational Technology, 7(4),100-107 (2008). [2]. Podlubny I., “Fractional differential equations “, ( Academic Press, 1990).
Nonlinear distributional geometry and Colombeau analysis of gravitation singularities in distributional general relativity with distributional Levi-Civit‘a connection
Jaykov Foukzon, Israel Institute of Technology, Haifa, Israel, math, Israel
Abstract: It seemed natural to identify gravitation singularities with singular values of the metric or curvature components and their scalar combinations [1]. However, under formal and mathematically abnormal calculation which known from a very old physics handbooks [2]-[3], such a notion depends on choosing a reference frame and includes fictious singularities which being real for some observers are absent for others.In a nutshell, there is a widespread belief that there exist true physical singularities and unphysical,i.e.,coordinate singularities. We try to base our approach to the problem of the gravitation singularities on the fact that a gravitation singularity leads by a natural way, directly to a singularity of a space-time structure in sense of Colombeau distributional geometry [4]-[6].We aim to describe gravitation singularities using mathematically rigorous approach via Colombeau nonlinear distributional space-time structures with distributional Levi-Civit‘a connection.We pointed out that some important physical singularities which many years mistakenly considered as coordinate singularities. [7]-[8] [1] D. Ivanenko and G. Sardanashvily,Foliation analysis of gravitation singularities, Physics Letters A Volume 91, Issue 7, 27 September 1982, Pages 341-344. https://doi.org/10.1016/0375-9601(82)90428-5 [2] L. D. Landau and E. M. Lifshitz, The Classical Theory of Fields, 7th ed. (Nauka, Moscow, 1988; Pergamon, Oxford,1975). [3] C. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation (Freeman, New York, 1973; Mir, Moscow, 1977). [4] M, Kunzinger, R. Steinbauer,Foundations of a Nonlinear Distributional Geometry, Acta Applicandae Mathematica,April 2002, Volume 71, Issue 2, pp 179–206. [5] J.A. Vickers,Distributional geometry in general relativity,Journal of Geometry and Physics 62 (2012) 692–705. [6] R. Steinbauer, Nonlinear distributional geometry and general relativity, https://arxiv.org/abs/math-ph/0104041v1 [7] J. Foukzon,Distributional Schwarzschild Geometry from Non Smooth Regularization Via Horizon,British Journal of Mathematics & Computer Science, ISSN: 2231-0851, 11(1): 1-28, 2015, Article no.BJMCS.16961,DOI : 10.9734/BJMCS/2015/16961 [8] J. Foukzon, A. Potapov and E. Menkova,Distributional SAdS BH-Spacetime Induced Vacuum Dominance,British Journal of Mathematics & Computer Science 13(6):1-54, 2016, Article no.BJMCS.19235,DOI:10.9734/BJMCS/2016/19235
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