Have a personal or library account? Click to login
Existence result for a fractional differential equation involving a special derivative Cover

Existence result for a fractional differential equation involving a special derivative

Open Access
|Jan 2022

References

  1. [1] R. P. Agarwal, M. Meehan, D. O’Regan, Fixed Point Theory and Applications, Cambridge Tracts in Mathematics, Cambridge University Press, Cambridge (2001).
  2. [2] R. R. Akhmerov, M. I. Kamenskii, A. S. Potapov, A. E Rodkina., B. N Sadovskii., Measures of Noncompactness and Condensing Operators, Birkhauser, Boston, Basel, Berlin (1992).10.1007/978-3-0348-5727-7
  3. [3] A. Arara, M. Benchohra, N. Hamidi, J. J. Nieto, Fractional order differential equations on an unbounded domain, Nonlinear Anal., 72(2010), 580-586.10.1016/j.na.2009.06.106
  4. [4] K. Balachandran, S. Kiruthika, J. J. Trujillo, Existence results for fractional impulsive integrodifferential equations in Banach spaces, Commun. Nonlinear Sci. Numer. Simul., 16(2011), 1970-1977.10.1016/j.cnsns.2010.08.005
  5. [5] K. Balachandran, J. Y. Park, nonlocal Cauchy problem for abstract fractional semilinear evolution equations, Nonlinear Anal., 71(2009), 4471-4475.10.1016/j.na.2009.03.005
  6. [6] K. Balachandran, J. J. Trujillo, The nonlocal Cauchy problem for nonlinear fractional integro-differential equations in Banach spaces, Nonlinear Anal., 72(2010), 4587-4593.10.1016/j.na.2010.02.035
  7. [7] J. Banas, K. Goebel, Measure of Noncompactness in Banach Spaces, 50. Lectures Notes in Pure and Applied Mathematics, Marcel Dekker, New York (1980).
  8. [8] K. Diethelm, Analysis of Fractional Differential Equations, Springer-Verlag, Berlin (2010).10.1007/978-3-642-14574-2
  9. [9] K. M. Furati, M. D. Kassim, N. E. Tatar, Existence and uniqueness for a problem involving Hilfer fractional derivative, Comput. Math. Appl., 64(2012), 1616-1626.10.1016/j.camwa.2012.01.009
  10. [10] L. Gaul, P. Klein, S. Kempfle, Damping description involving fractional operators, Mech. Systems Signal Processing, 5(1991), 81-88.10.1016/0888-3270(91)90016-X
  11. [11] D. J. Guo, V. Lakshmikantham, X. Liu, Nonlinear Integral Equations in Abstract Spaces, Kluwer Academic Publishers, Dordrecht (1996).10.1007/978-1-4613-1281-9
  12. [12] A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and Applications of Fractional Differential Equations, North-Holland Mathematics Studies, 204. Elsevier Science B.V., Amsterdam (2006).
  13. [13] C. Kou, j. Liu, y. Ye, Existence and uniqueness of solutions for the Cauchy-type problems of fractional differential equations, Discrete Dynamics in Nature and Society 2010 (2010) 1-15.10.1155/2010/142175
  14. [14] F. Metzler, W. Schick, H. G. Kilian, T.F. Nonnenmacher, Relaxation in filled polymers: A fractional calculus approach, J. Chem. Phys., 103(1995), 7180-7186.10.1063/1.470346
  15. [15] K. S. Miller, B. Ross, An Introduction to the Fractional Calculus and Differential Equations, John Wiley, New York (1993).
  16. [16] I. Podlubny, Fractional Differential Equations, Academic Press, San Diego (1999).
  17. [17] H. A. H. Salem, On the fractional calculus in abstract spaces and their applications to the Dirichlet-type problem of fractional order, Comput. Math. Appl., 59(2010), 1278-1293.10.1016/j.camwa.2009.06.025
  18. [18] S. G. Samko, A. A. Kilbas, O. I. Marichev, Fractional Integrals and Derivatives Theory and Applications, Gordon and Breach, Amsterdam, 1987, Engl. Trans.
  19. [19] J. M. A. Toledano, T. D. Benavides, G. L. Azedo, Measures of Noncompactness in Metric Fixed Point Theory, Birkhauser, Basel (1997).10.1007/978-3-0348-8920-9
  20. [20] Y. Zhou, Basic Theory of Fractional Differential Equations, World Scientific, Singapore (2014).10.1142/9069
Language: English
Page range: 67 - 77
Submitted on: Dec 31, 2020
|
Accepted on: May 12, 2021
|
Published on: Jan 13, 2022
Published by: Sciendo
In partnership with: Paradigm Publishing Services
Publication frequency: 3 issues per year

© 2022 Moustafa Beddani, Benaouda Hedia, published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.