Boundary value problems for Caputo-Hadamard fractional differential inclusions in Banach spaces

Amouria Hammou; Samira Hamani; Johnny Henderson

Archivum Mathematicum (2022)

  • Volume: 058, Issue: 4, page 227-240
  • ISSN: 0044-8753

Abstract

top
In this article, we study the existence of solutions in a Banach space of boundary value problems for Caputo-Hadamard fractional differential inclusions of order r ∈ ( 0 , 1 ] .

How to cite

top

Hammou, Amouria, Hamani, Samira, and Henderson, Johnny. "Boundary value problems for Caputo-Hadamard fractional differential inclusions in Banach spaces." Archivum Mathematicum 058.4 (2022): 227-240. <http://eudml.org/doc/298911>.

@article{Hammou2022,
abstract = {In this article, we study the existence of solutions in a Banach space of boundary value problems for Caputo-Hadamard fractional differential inclusions of order $r \in (0,1]$.},
author = {Hammou, Amouria, Hamani, Samira, Henderson, Johnny},
journal = {Archivum Mathematicum},
keywords = {fractional differential inclusion; Caputo-Hadamard fractional derivative; Mönch’s fixed point theorem; Kuratowski measure of noncompactness},
language = {eng},
number = {4},
pages = {227-240},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Boundary value problems for Caputo-Hadamard fractional differential inclusions in Banach spaces},
url = {http://eudml.org/doc/298911},
volume = {058},
year = {2022},
}

TY - JOUR
AU - Hammou, Amouria
AU - Hamani, Samira
AU - Henderson, Johnny
TI - Boundary value problems for Caputo-Hadamard fractional differential inclusions in Banach spaces
JO - Archivum Mathematicum
PY - 2022
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 058
IS - 4
SP - 227
EP - 240
AB - In this article, we study the existence of solutions in a Banach space of boundary value problems for Caputo-Hadamard fractional differential inclusions of order $r \in (0,1]$.
LA - eng
KW - fractional differential inclusion; Caputo-Hadamard fractional derivative; Mönch’s fixed point theorem; Kuratowski measure of noncompactness
UR - http://eudml.org/doc/298911
ER -

References

top
  1. Adjabi, Y., Jarad, F., Baleanu, D., Abdeljawad, T., On Cauchy problems with Caputo Hadamard fractional derivatives, J. Comput. Anal. Appl. 21 (4) (2016), 661–681. (2016) MR3495061
  2. Agarwal, R.P., Benchohra, M., Seba, D., 10.1007/s00025-009-0434-5, Results Math. 55 (2009), 221–230. (2009) MR2571191DOI10.1007/s00025-009-0434-5
  3. Ahmad, B., Khan, R.A., Sivasundaram, S., Generalized quasilinearization method for a first order differential equation with integral boundary condition, Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal. 12 (2) (2005), 289–296. (2005) Zbl1084.34007MR2170414
  4. Ahmad, B., Ntouyas, S.K., Initial value problems for hybrid Hadamard fractional equations, Electron. J. Differential Equ. 2014 (161) (2014), 8 pp. (2014) MR3239404
  5. Akhmerov, R.R., Kamenski, M.I., Patapov, A.S., Rodkina, A.E., Sadovski, B.N., Measures of noncompactness and condensing operators (Translated from the 1986 Russian original by A. Iacop), Operator theory: Advances and Applications, ranslated from the 1986 russian original by a. iacop), operator theory: advances and applications, vol. 55, Birkhäuser Verlag, Basel, 1992. (1992) MR1153247
  6. Aubin, J.P., Cellina, A., Differential inclusions, Springer-Verlag, Berlin-Heidelberg, New York, 1984. (1984) MR0755330
  7. Aubin, J.P., Frankowska, H., Set-valued analysis, Birkhäuser, Boston, 1990. (1990) MR1048347
  8. Banas, J., Goebel, K., Measure of noncompactness in Banach spaces, Lecture Notes in Pure and Appl. Math., Marcel Dekker, New York, 1980. (1980) MR0591679
  9. Belarbi, A., Benchohra, M., Existence results for nonlinear boundary-value problems with integral boundary conditions, Electron. J. Differential Equ. 6 (2005), 1–10. (2005) MR2119058
  10. Benchohra, M., Hamani, S., 10.7151/dmdico.1099, Discuss. Math. Differ. Incl. Control Optim. 28 (2008), 147–164. (2008) Zbl1181.26012MR2548782DOI10.7151/dmdico.1099
  11. Benchohra, M., Hamani, S., Nonlinear boundary value problems for differential inclusions with Caputo fractional derivative, Topol. Methods Nonlinear Anal. 32 (1) (2008), 115–130. (2008) Zbl1180.26002MR2466806
  12. Benchohra, M., Henderson, J., Seba, D., Measure of noncompactness and fractional differential equations in Banach spaces, Commun. Appl. Anal. 12 (2008), 419–428. (2008) MR2494987
  13. Benchohra, M., Henderson, J., Seba, D., Measure of noncompactness and fractional andhyperbolic partial fractional differential equations in Banach space, PanAmer. Math. J. 20 (2010), 27–37. (2010) MR2760586
  14. Benchohra, M., Henderson, J., Seba, D., Boundary value problems for fractional differential inclusions in Banach space, Fract. Differ. Calc. 2 (2012), 99–108. (2012) MR3003005
  15. Benhamida, W., Hamani, S., Measure of noncompactness and Caputo-Hadamard fractional differantial equations in Banach spaces, Eur. Bull. Math. 1 (3) (2018), 98–103. (2018) 
  16. Benhamida, W., Hamani, S., Henderson, J., Boundary value problems for Caputo-Hadamard fractional differential equations, Adv. Theor. Nonlinear Anal. Appl. 2 (3) (2018), 138–145. (2018) MR3957191
  17. Brykalov, S.A., 10.1515/GMJ.1994.243, Georgian Math. J. 1 (1994), 243–249. (1994) Zbl0807.34021MR1262564DOI10.1515/GMJ.1994.243
  18. Butzer, P.L., Kilbas, A.A., Trujillo, J.J., 10.1016/S0022-247X(02)00049-5, J. Math. Anal. Appl. 269 (2002), 387–400. (2002) MR1907120DOI10.1016/S0022-247X(02)00049-5
  19. Butzer, P.L., Kilbas, A.A., Trujillo, J.J., 10.1016/S0022-247X(02)00001-X, J. Math. Anal. Appl. 269 (2002), 1–27. (2002) Zbl0995.26007MR1907871DOI10.1016/S0022-247X(02)00001-X
  20. Butzer, P.L., Kilbas, A.A., Trujillo, J.J., 10.1016/S0022-247X(02)00066-5, J. Math. Anal. Appl. 270 (2002), 1–15. (2002) Zbl1022.26011MR1911748DOI10.1016/S0022-247X(02)00066-5
  21. Deimling, .K., Multivalued differential equations, Walter De Gruyter, Berlin-New York, 1992. (1992) MR1189795
  22. Denche, M., Marhoune, A.L., High order mixed-type differential equations with weighted integral boundary conditions, Electron. J. Differential Equ. 2000 (60) (2000), 1–10. (2000) MR1787207
  23. Diethelm, K., Freed, A.D., On the solution of nonlinear fractional order differential equations used in the modeling of viscoplasticity, Scientifice Computing in Chemical Engineering II-Computational Fluid Dynamics, Reaction Engineering and Molecular Properties (Keil, F., Mackens, W., Voss, H., Werther, J., eds.), Springer-Verlag, Heidelberg, 1999, pp. 217–224. (1999) MR1415870
  24. Gallardo, J.M., Second order differential operators with integral boundary conditions and generation of semigroups, Rocky Mountain J. Math. 30 (2000), 1265–1292. (2000) MR1810167
  25. Gambo, Y.Y., Jarad, F., Baleanu, D., Abdeljawad, T., On Caputo modification of the Hadamard fractional derivatives, Adv. Difference Equ. 2014 (10) (2014), 12 pp. (2014) MR3213915
  26. Gaul, L., Klein, P., Kempfle, S., 10.1016/0888-3270(91)90016-X, Mech. Systems Signal Processing 5 (1991), 81–88. (1991) DOI10.1016/0888-3270(91)90016-X
  27. Glockle, W.G., Nonnenmacher, T.F., 10.1016/S0006-3495(95)80157-8, Biophys. J. 68 (1995), 46–53. (1995) DOI10.1016/S0006-3495(95)80157-8
  28. Hadamard, J., Essai sur l’étude des fonctions donnees par leur development de Taylor, J. Math. Pure Appl. 8 (1892), 101–186. (1892) 
  29. Hilfer, R., Applications of fractional calculus in physics, World Scientific, Singapore, 2000. (2000) Zbl0998.26002MR1890104
  30. Jarad, F., Abdeljawad, T., Baleanu, D., Caputo-type modification of the Hadamard fractional derivatives, Adv. Difference Equ. 2012 (142) (2012), 8 pp. (2012) MR2992066
  31. Karakostas, G.L., Tsamatos, P.Ch., Multiple positive solutions of some Fredholm integral equations arisen from nonlocal boundary value problems, Electron. J. Differential Equ. 2002 (30) (2002), 1–17. (2002) MR1907706
  32. Khan, R. A., 10.14232/ejqtde.2003.1.19, Electron. J. Qual. Theory Differ. Equ. 2003 (10) (2003), 1–15. (2003) Zbl1055.34033MR2039793DOI10.14232/ejqtde.2003.1.19
  33. Kilbas, A.A., Hadamard-type fractional calculus, J. Korean Math. Soc. 38 (6) (2001), 1191–1204. (2001) MR1858760
  34. Kilbas, A.A., Srivastava, H.M., Trujillo, J.J., Theory and applications of fractional differential equations, North-Holland Math. Studies, Elsevier Science B.V., Amsterdam, 2006. (2006) MR2218073
  35. Klimek, M., 10.1016/j.cnsns.2011.01.018, Commun. Nonlinear Sci. Numer. Simul. 16 (12) (2011), 4689–4697. (2011) MR2820858DOI10.1016/j.cnsns.2011.01.018
  36. Krall, A.M., 10.1090/S0002-9939-1965-0181794-9, Proc. Amer. Math. Soc. 16 (1965), 738–742. (1965) MR0181794DOI10.1090/S0002-9939-1965-0181794-9
  37. Lomtatidze, A., Malaguti, L., 10.1515/GMJ.2000.133, Georgian Math. J. 7 (2000), 133–154. (2000) MR1768050DOI10.1515/GMJ.2000.133
  38. Mainardi, F., Fractional calculus: Some basic problems in continuum and statistical mechanics, Fractals and Fractional Calculus in Continuum Mechanics (Carpinteri, A., Mainardi, F., eds.), Springer-Verlag, Wien, 1997, pp. 291–348. (1997) MR1611587
  39. Metzler, F., Schick, W., Kilian, H.G., Nonnenmacher, T.F., 10.1063/1.470346, J. Chem. Phys. 103 (1995), 7180–7186. (1995) DOI10.1063/1.470346
  40. Miller, K.S., Ross, B., An introduction to the fractional calculus and differential equations, John Wiley, New York, 1993. (1993) MR1219954
  41. Oldham, K.B., Spanier, J., The fractional calculus, Academic Press, New York, London, 1974. (1974) MR0361633
  42. O’Regan, D., Precup, R., 10.1006/jmaa.2000.6789, J. Math. Anal. Appl. 245 (2000), 594–612. (2000) MR1758558DOI10.1006/jmaa.2000.6789
  43. Thiramanus, P., Ntouyas, S.K., Tariboon, J., xistence and uniqueness results for Hadamard-type fractional differential equations with nonlocal fractional integral boundary conditions, Abstr. Appl. Anal. 2014 (2014), 9 pp., Art. ID 902054. (2014) MR3228094

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.