Skip to main content Skip to main navigation menu Skip to site footer
  • Login
  • Language
    • English
    • Język Polski
  • Menu
  • Home
  • Current
  • Online First
  • Archives
  • About
    • About the Journal
    • Submissions
    • Editorial Team
    • Privacy Statement
    • Contact
  • Login
  • Language:
  • English
  • Język Polski

Topological Methods in Nonlinear Analysis

Generalized fractional differential equations and inclusions equipped with nonlocal generalized fractional integral boundary conditions
  • Home
  • /
  • Generalized fractional differential equations and inclusions equipped with nonlocal generalized fractional integral boundary conditions
  1. Home /
  2. Archives /
  3. Vol 54, No 2B (December 2019) /
  4. Articles

Generalized fractional differential equations and inclusions equipped with nonlocal generalized fractional integral boundary conditions

Authors

  • Sotiris K. Ntouyas https://orcid.org/0000-0002-7695-2118
  • Bashir Ahmad https://orcid.org/0000-0001-5350-2977
  • Madeaha Alghanmi
  • Ahmed Alsaedi https://orcid.org/0000-0003-3452-8922

Keywords

Differential Equation, Caputo fractional derivative, fractional integral, existence, fixed point

Abstract

In this paper, we establish sufficient criteria for the existence of solutions for generalized fractional differential equations and inclusions supplemented with generalized fractional integral boundary conditions. We make use of the standard fixed point theorems for single-valued and multivalued maps to obtain the desired results, which are well illustrated with the aid of examples.

References

R.P. Agarwal, Y. Zhou, J.R. Wang and X. Luo, Fractional functional differential equations with causal operators in Banach spaces, Math. Comput. Modelling 54 (2011), 1440–1452.

B. Ahmad, A. Alsaedi, S. Aljoudi and S.K. Ntouyas, On a coupled system of sequential fractional differential equations with variable coefficients and coupled integral boundary conditions, Bull. Math. Soc. Sci. Math. Roumanie (N.S.) 60 (2017), no. 108, 3–18.

B. Ahmad, A. Alsaedi, S.K. Ntouyas and J. Tariboon, Hadamard-Type Fractional Differential Equations, Inclusions and Inequalities, Springer, Cham, 2017.

B. Ahmad and S.K. Ntouyas, Existence results for a coupled system of Caputo type sequential fractional differential equations with nonlocal integral boundary conditions, Appl. Math. Comput. 266 (2015), 615–622.

B. Ahmad and S.K. Ntouyas, Existence results for fractional differential inclusions with Erdelyi–Kober fractional integral conditions, An. Ştiinţ. Univ. “Ovidius” Constanţa Ser. Mat. 25 (2017), 5–24.

B. Ahmad, S.K. Ntouyas and A. Alsaedi, New existence results for nonlinear fractional differential equations with three-point integral boundary conditions, Adv. Difference Equ. (2011), Art. ID 107384, 11 pp.

B. Ahmad, S.K. Ntouyas and J. Tariboon, A study of mixed Hadamard and RiemannLiouville fractional integro-differential inclusions via endpoint theory, Appl. Math. Lett. 52 (2016), 9–14.

M. Benchohra, J. Henderson, S.K. Ntouyas and A. Ouahab, Existence results for fractional order functional differential equations with infinite delay, J. Math. Anal. Appl. 338 (2008), 1340–1350.

C. Castaing and M. Valadier, Convex Analysis and Measurable Multifunctions, Lecture Notes in Mathematics, vol. 580, Springer–Verlag, Berlin, Heidelberg, New York, 1977.

H. Covitz and S.B. Nadler Jr., Multivalued contraction mappings in generalized metric spaces, Israel J. Math. 8 (1970), 5–11.

K. Deimling, Multivalued Differential Equations, Walter De Gruyter, Berlin, New York, 1992.

K. Diethelm, The Analysis of Fractional Differential Equations, Lecture Notes in Mathematics, Springer–Verlag, Berlin, Heidelberg, 2010.

A. Granas and J. Dugundji, Fixed Point Theory, Springer–Verlag, New York, 2003.

Sh. Hu and N. Papageorgiou, Handbook of Multivalued Analysis, Volume I. Theory, Kluwer, Dordrecht, 1997.

U.N. Katugampola, New Approach to a generalized fractional integral, Appl. Math. Comput. 218 (2015), 860–865.

U.N. Katugampola, A new approach to generalized fractional derivatives, Bull. Math, Anal. Appl.

A.A. Kilbas, H.M. Srivastava and J.J. Trujillo, Theory and Applications of Fractional Differential Equations, North-Holland Mathematics Studies, vol. 204, Elsevier Science B.V., Amsterdam, 2006.

M. Kisielewicz, Stochastic Differential Inclusions and Applications, Springer Optimization and Its Applications, vol. 80, Springer, New York, 2013.

M.A. Krasnosel’skiı̆, Two remarks on the method of successive approximations, Uspekhi Mat. Nauk 10 (1955), 123–127.

V. Lakshmikantham, S. Leela and J.V. Devi, Theory of Fractional Dynamic Systems, Cambridge Academic Publishers, Cambridge, 2009.

A. Lasota and Z. Opial, An application of the Kakutani–Ky Fan theorem in the theory of ordinary differential equations, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys. 13 (1965), 781–786.

B. Lupinska and T. Odzijewicz, A Lyapunov-type inequality with the Katugampolafractional derivative, Math. Meth. Appl. Sci. (2018), 1–12.

K.S. Miller and B. Ross, An Introduction to the Fractional Calculus and Differential Equations, John Wiley, New York, 1993.

I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999.

Downloads

  • PREVIEW
  • FULL TEXT

Published

2019-07-13

How to Cite

1.
NTOUYAS, Sotiris K., AHMAD, Bashir, ALGHANMI, Madeaha and ALSAEDI, Ahmed. Generalized fractional differential equations and inclusions equipped with nonlocal generalized fractional integral boundary conditions. Topological Methods in Nonlinear Analysis. Online. 13 July 2019. Vol. 54, no. 2B, pp. 1051 - 1073. [Accessed 8 June 2026].
  • ISO 690
  • ACM
  • ACS
  • APA
  • ABNT
  • Chicago
  • Harvard
  • IEEE
  • MLA
  • Turabian
  • Vancouver
Download Citation
  • Endnote/Zotero/Mendeley (RIS)
  • BibTeX

Issue

Vol 54, No 2B (December 2019)

Section

Articles

Stats

Number of views and downloads: 0
Number of citations: 0

Search

Search

Browse

  • Browse Author Index
  • Issue archive

User

User

Current Issue

  • Atom logo
  • RSS2 logo
  • RSS1 logo

Newsletter

Subscribe Unsubscribe
Up

Akademicka Platforma Czasopism

Najlepsze czasopisma naukowe i akademickie w jednym miejscu

apcz.umk.pl

Partners

  • Akademia Ignatianum w Krakowie
  • Akademickie Towarzystwo Andragogiczne
  • Fundacja Copernicus na rzecz Rozwoju Badań Naukowych
  • Instytut Historii im. Tadeusza Manteuffla Polskiej Akademii Nauk
  • Instytut Kultur Śródziemnomorskich i Orientalnych PAN
  • Instytut Tomistyczny
  • Karmelitański Instytut Duchowości w Krakowie
  • Ministerstwo Kultury i Dziedzictwa Narodowego
  • Państwowa Akademia Nauk Stosowanych w Krośnie
  • Państwowa Akademia Nauk Stosowanych we Włocławku
  • Państwowa Wyższa Szkoła Zawodowa im. Stanisława Pigonia w Krośnie
  • Polska Fundacja Przemysłu Kosmicznego
  • Polskie Towarzystwo Ekonomiczne
  • Polskie Towarzystwo Ludoznawcze
  • Towarzystwo Miłośników Torunia
  • Towarzystwo Naukowe w Toruniu
  • Uniwersytet im. Adama Mickiewicza w Poznaniu
  • Uniwersytet Komisji Edukacji Narodowej w Krakowie
  • Uniwersytet Mikołaja Kopernika
  • Uniwersytet w Białymstoku
  • Uniwersytet Warszawski
  • Wojewódzka Biblioteka Publiczna - Książnica Kopernikańska
  • Wyższe Seminarium Duchowne w Pelplinie / Wydawnictwo Diecezjalne „Bernardinum" w Pelplinie

© 2021- Nicolaus Copernicus University Accessibility statement Shop