Existence and Ulam Stability for Partial Impulsive Discontinuous Fractional Differential Inclusions in Banach Algebras

详细信息    查看全文

• 作者：Sa?d Abbas ; Mouffak Benchohra
• 关键词：26A33 ; 34G20 ; 34A40 ; 45N05 ; 47H10 ; Partial fractional differential inclusion ; left ; sided mixed Riemann–Liouville integral ; Caputo fractional ; order derivative ; fixed point inclusion ; Banach algebra ; impulse ; Ulam–Hyers stability
• 刊名：Mediterranean Journal of Mathematics
• 出版年：2015
• 出版时间：November 2015
• 年：2015
• 卷：12
• 期：4
• 页码：1245-1264
• 全文大小：625 KB
• 参考文献：1.Abbas, S., Agarwal, R.P., Benchohra, M.: Impulsive discontinuous partial hyperbolic differential equations of fractional order on Banach algebras. Electron. J. Differ. Equ. 2010(91), 17
  2.Abbas S., Benchohra M.: Partial hyperbolic differential equations with finite delay involving the Caputo fractional derivative. Commun. Math. Anal. 7, 62-2 (2009)MATH MathSciNet
  3.Abbas S., Benchohra M.: Impulsive partial hyperbolic functional differential equations of fractional order with state-dependent delay. Frac. Calc. Appl. Anal. 13(3), 225-44 (2010)MATH MathSciNet
  4.Abbas S., Benchohra M.: Upper and lower solutions method for impulsive partial hyperbolic differential equations with fractional order. Nonlinear Anal. Hybrid Syst. 4, 604-13 (2010)
  5.Abbas S., Benchohra M.: Impulsive partial hyperbolic differential inclusions of fractional order. Demonstratio Math. XLIII 4, 775-97 (2010)
  6.Abbas S., Benchohra M., Gorniewicz L.: Fractional order impulsive partial hyperbolic differential inclusions with variable times. Discuss. Math. Differ. Incl. Control Optim. 31(1), 91-14 (2011)MATH MathSciNet CrossRef
  7.Abbas, S., Benchohra, M., N’Guérékata, G.M.: Topics in Fractional Differential Equations. Springer, New York (2012)
  8.Abbas S., Benchohra M., N’Guérékata G.M., Slimani B.A.: Darboux problem for fractional order discontinuous hyperbolic partial differential equations in Banach algebras. Complex Var. Elliptic Equ. 57(2-), 337-50 (2012)MATH MathSciNet CrossRef
  9.Bota-Boriceanu M.F., Petrusel A.: Ulam–Hyers stability for operatorial equations and inclusions. Anal. Univ. I. Cuza Iasi 57, 65-4 (2011)MATH MathSciNet
  10.Castro L.P., Ramos A.: Hyers–Ulam–Rassias stability for a class of Volterra integral equations. Banach J. Math. Anal. 3, 36-3 (2009)MathSciNet CrossRef
  11.Dhage B.C.: Existence results for neutral functional differential inclusions in Banach algebras. Nonlinear Anal. 64, 1290-306 (2006)MATH MathSciNet CrossRef
  12.Hilfer, R.: Applications of Fractional Calculus in Physics. World Scientific, Singapore (2000)
  13.Hyers D.H.: On the stability of the linear functional equation. Proc. Natl. Acad. Sci. 27, 222-24 (1941)MathSciNet CrossRef
  14.Hyers, D.H., Isac, G., Rassias, T.H.M.: Stability of Functional Equations in Several Variables. Birkhauser, Boston (1998)
  15.Jung, S.-M.: Hyers–Ulam–Rassias Stability of Functional Equations in Mathematical Analysis. Hadronic Press, Palm Harbor (2001)
  16.Jung, S.-M.: Hyers–Ulam–Rassias Stability of Functional Equations in Nonlinear Analysis. Springer, New York (2011)
  17.Jung, S.-M.: A fixed point approach to the stability of a Volterra integral equation. Fixed Point Theory Appl. 2007, 1 (2007) (article ID 57064)
  18.Hu, S.H., Papageorgiou, N.: Handbook of Multivalued Analysis, Theory I. Kluwer, Dordrecht (1997)
  19.Kilbas, A.A., Srivastava, H.M., Trujillo, J.J.: Theory and Applications of Fractional Differential Equations. North-Holland Mathematics Studies, 204. Elsevier Science B.V., Amsterdam (2006)
  20.Lakshmikantham, V., Bainov, D.D., Simeonov, P.S.: Theory of Impulsive Differential Equations. World Scientific, Singapore (1989)
  21.Lasota A., Opial Z.: An application of the KakutaniKy Fan theorem in the theory of ordinary differential equations. Bull. Acad. Pol. Sci. Ser. Sci. Math. Astronom. Phys. 13, 781-86 (1965)MATH MathSciNet
  22.Li, X., Wang, J.: Ulam–Hyers–Rassias stability of semilinear differential equations with impulses. Electron. J. Differ. Equ. 2013(172), 8
  23.Miller, K.S., Ross, B.: An Introduction to the Fractional Calculus and Differential Equations. Wiley, New York (1993)
  24.Petru T.P., Bota M.-F.: Ulam–Hyers stabillity of operational inclusions in complete gauge spaces. Fixed Point Theory 13, 641-50 (2012)MATH MathSciNet
  25.Petru T.P., Petrusel A., Yao J.-C.: Ulam0-Hyers stability for operatorial equations and inclusions via nonself operators. Taiwan. J. Math. 15, 2169-193 (2011)MathSciNet
  26.Podlubny, I.: Fractional Differential Equations. Academic Press, San Diego (1999)
  27.Rassias T.H.M.: On the stability of linear mappings in Banach spaces. Proc. Am. Math. Soc. 72, 297-00 (1978)MATH CrossRef
  28.Rus I.A.: Ulam stability of ordinary differential equations. Stud. Univ. Babes-Bolyai, Math. LIV 4, 125-33 (2009)MathSciNet
  29.Rus I.A.: Remarks on Ulam stability of the operatorial equations. Fixed Point Theory 10, 305-20 (2009)MATH MathSciNet
  30.Samoilenko, A.M., Perestyuk, N.A.: Impulsive Differential Equations. World Scientific, Singapore (1995)
  31.Ulam, S.M.: A Collection of Mathematical Problems. Interscience Publishers, New York (1968)
  32.Vityuk A.N., Golushkov A.V.: Existence of solutions of systems of partial differential equations of fractional order. Nonlinear Oscil. 7(3), 318-25 (2004)MathSciNet CrossRef
  33.Vityuk, A.N., Mykhailenko, A.V.: The Darboux problem for an implicit fractional-order differential equation. J. Math. Sci. 1
• 作者单位：Sa?d Abbas (1)
  Mouffak Benchohra (2) (3)
  
  1. 10-320 de Salaberry, Montréal, QC, H3M 1K9, Canada
  2. Laboratoire de Mathématiques, Université de Sidi Bel-Abbès, B.P. 89, 22000, Sidi Bel-Abbès, Algeria
  3. Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  
• 出版者：Birkh盲user Basel
• ISSN：1660-5454

文摘

In this paper, we investigate some existence and Ulam’s type stability concepts of fixed point inclusions for a class of partial discontinuous fractional-order differential inclusions with impulses in Banach Algebras. Our results are obtained using weakly Picard operators theory. Mathematics Subject Classification 26A33 34G20 34A40 45N05 47H10