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Tytuł artykułu
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Warianty tytułu
Języki publikacji
Abstrakty
We investigate some existence and stability results for the Darboux problem of partial fractional random differential equations in Banach spaces. Our existence results are based upon some fixed point theorems.
Słowa kluczowe
Wydawca
Czasopismo
Rocznik
Tom
Strony
79--87
Opis fizyczny
Bibliogr. 23 poz.
Twórcy
autor
- Laboratory of Mathematics, University of Saïda, P.O. Box 138, 20000 Saïda, Algeria
autor
- Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia
autor
- Laboratory of Mathematics, University of Sidi Bel-Abbès, P.O. Box 89, 22000 Sidi Bel-Abbès, Algeria
- Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia
autor
- Department of Mathematics, Sciences Faculty for Girls, King Abdulaziz University, Jeddah, Saudi Arabia
Bibliografia
- [1] S. Abbas, D. Baleanu and M. Benchohra, Global attractivity for fractional order delay partial integro-differential equations, Adv. Difference Equ. 2012 (2012), Article ID 62.
- [2] S. Abbas and M. Benchohra, Darboux problem for perturbed partial differential equations of fractional order with finite delay, Nonlinear Anal. Hybrid Syst. 3 (2009), 597–604.
- [3] S. Abbas, M. Benchohra and J. Henderson, Asymptotic attractive nonlinear fractional order Riemann–Liouville integral equations in Banach algebras, Nonlinear Stud. 20 (2013), 1–10.
- [4] S. Abbas, M. Benchohra and G. M. N’Guérékata, Topics in Fractional Differential Equations, Springer, New York, 2012.
- [5] S. Abbas, M. Benchohra and G. M. N’Guérékata, Advanced Fractional Differential and Integral Equations, Nova Science Publishers, New York, 2015.
- [6] S. Abbas, M. Benchohra and J. J. Nieto, Global attractivity of solutions for nonlinear fractional order Riemann–Liouville Volterra-Stieltjes partial integral equations, Electron. J. Qual. Theory Differ. Equ. 81 (2012), 1–15.
- [7] J. Banas and B. C. Dhage, Global asymptotic stability of solutions of a functional integral equation, Nonlinear Anal. 69 (2008), no. 7, 1945–1952.
- [8] T. A. Burton, T. Furumochi, A note on stability by Schauder’s theorem, Funkcial. Ekvac. 44 (2001), 73–82.
- [9] J. Charrier, Strong and weak error estimates for elliptic partial differential equations with random coefficients, SIAM. J. Numer. Anal 50 (2012), 216–246.
- [10] C. Corduneanu, Integral Equations and Stability of Feedback Systems, Academic Press, New York, 1973.
- [11] B. C. Dhage, S. V. Badgire and S. K. Ntouyas, Periodic boundary value problems of second order random differential equations, Electron. J. Qual. Theory Differ. Equ. 21 (2009), 1–14.
- [12] X. Han, X. Ma and G. Dai, Solutions to fourth-order random differential equations with periodic boundary conditions, Electron. J. Differential Equations 235 (2012), 1–9.
- [13] S. Itoh, Random fixed point theorems with applications to random differential equations in Banach spaces, J. Math. Anal. Appl. 67 (1979), 261–273.
- [14] A. A. Kilbas, H. M. Srivastava and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, North-Holland Math. Stud. 204, Elsevier, Amsterdam, 2006.
- [15] C. Li, R. Sun and J. Sun, Stability analysis of a class of stochastic differential delay equations with nonlinear impulsive effects, J. Franklin Inst. 347 (2010), 1186–1198.
- [16] J. Li, J. Shi and J. Sun, Stability of impulsive stochastic diff0erential delay systems and application to impulsive stochastic neutral networks, Nonlinear Anal. 74 (2011), 3099–3111.
- [17] B. Liu, Stability of solutions for stochastic impulsive systems via comparison approach, IEEE Trans. Automat. Control 53 (2008), 2128–2133.
- [18] G. S. Priya, P. Prakash, J. J. Nieto and Z. Kayar, Higher-order numerical scheme for the fractional heat equation with Dirichlet and Neumann boundary conditions, NNum. Heat Transfer B Fundam. 63 (2013), 540–559.
- [19] T. T. Soong, Random Differential Equations in Science and Engineering, Academic Press, New York, 1973.
- [20] D. Stanescu and B.M. Chen-Charpentier, Random coefficient differential equation models for bacterial growth, Math. Comput. Model. 50 (2009), 885–895.
- [21] A. N. Vityuk and A. V. Golushkov, Existence of solutions of systems of partial differential equations of fractional order, Nonlinear Oscil. 7 (2004), no. 3, 318–325.
- [22] X. Yang, and J. Cao, Synchronization of delayed complex dynamical networks with impulsive and stochastic effects, Nonlinear Anal. Real World Appl. 12 (2011), 2252–2266.
- [23] D. P. Zielinski and V. R. Voller, A random walk solution for fractional diffusion equations, Internat. J. Numer. Methods Heat Fluid Flow 23 (2013), 7–22.
Typ dokumentu
Bibliografia
Identyfikator YADDA
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