Journal of the Korean Society for Industrial and Applied Mathematics

Korean Society for Industrial and Applied Mathematics (한국산업응용수학회)
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EXISTENCE OF SOLUTION FOR IMPULSIVE FRACTIONAL DIFFERENTIAL EQUATIONS VIA TOPOLOGICAL DEGREE METHOD

  • FAREE, TAGHAREED A. (DEPARTMENT OF MATHEMATICS, DR. BABASAHEB AMBEDKAR MARATHWADA UNIVERSITY) ;
  • PANCHAL, SATISH K. (DEPARTMENT OF MATHEMATICS, DR. BABASAHEB AMBEDKAR MARATHWADA UNIVERSITY)
  • Received : 2020.12.30
  • Accepted : 2021.03.24
  • Published : 2021.03.25
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Abstract

This paper is studied the existence of a solution for the impulsive Cauchy problem involving the Caputo fractional derivative in Banach space by using topological structures. We based on using topological degree method and fixed point theorem with some suitable conditions. Further, some topological properties for the set of solutions are considered. Finally, an example is presented to demonstrate our results.

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References

  1. A. A. Kilbas, H. M. Srivastava and J. J. Trujillo, Theory and applications of fractional differential equations, ser. North-Holland Mathematics Studies. Amsterdam: Elsevier, vol. 204, (2006).
  2. K.S. Miller and B. Ross, An Introduction to the Fractional Calculus and Differential Equations, John Wiley, New York, (1993).
  3. I. Podlubny , Fractional Differential Equation, Academic Press, San Diego, (1999).
  4. K. Deimling, Nonlinear Functional Analysis, Springer-Verlag, (1985).
  5. M. Feckan, Topological Degree Approach to Bifurcation Problems, Topological Fixed Point Theory and its Applications, vol. 5, (2008).
  6. J. Mawhin, Topological Degree Methods in Nonlinear Boundary Value Problems, CMBS Regional Conference Series in Mathematics, vol. 40, Amer. Math. Soc. , Providence, R. I. , (1979).
  7. R.P. Agarwal, Y. Zhou and Y. He, Existence of fractional neutral functional differential equations, Comput. Math. Appl, 59(2010), 1095-1100. https://doi.org/10.1016/j.camwa.2009.05.010
  8. K. Balachandran and J.Y. Park, Nonlocal Cauchy problem for abstract fractional semilinear evolution equations, Nonlinear Analysis, 71(2009), 4471-4475. https://doi.org/10.1016/j.na.2009.03.005
  9. S. Zhang, The existence of a positive solution for a nonlinear fractional differential equation, J. Math. Anal. Appl. 252(2000), 804-812. https://doi.org/10.1006/jmaa.2000.7123
  10. M. Benchohra and D. Seba, Impulsive fractional differential equations in Banach Spaces, Electronic Journal of Qualitative Theory of Differential Equations, (2009).
  11. B. Ahmad and S. Sivasundaram, Existence of solutions for impulsive integral boundary value problems of fractional order, Nonlinear Anal Hybrid Syst, 4(2010), 134-41. https://doi.org/10.1016/j.nahs.2009.09.002
  12. J. Wang, Y. Zhou and W. Wei, Study in fractional differential equations by means of topological degree methods, Numerical functional analysis and optimization, (2012).
  13. J. Wang, Y. Zhou and M. Medve, Qualitative analysis for nonlinear fractional differential equations via topological degree method, Topological methods in Nonlinear Analysis, 40(2)(2012), 245-271.
  14. M. Feckan, Y. Zhou and J. Wang, On the concept and existence of solution for impulsive fractional differential equations, Commun Nonlinear Sci Numer Simulat, 17(2012), 3050-3060. https://doi.org/10.1016/j.cnsns.2011.11.017
  15. Y. Zhou, Basic Theory Of Fractional Differential Equations, World Scientific, (2017).