Publication Cover
Applicable Analysis
An International Journal
Volume 101, 2022 - Issue 2
191
Views
7
CrossRef citations to date
0
Altmetric
Articles

Controllability of coupled systems for impulsive φ-Hilfer fractional integro-differential inclusions

, &
Pages 383-400 | Received 21 Jan 2020, Accepted 06 Mar 2020, Published online: 09 Apr 2020

References

  • Baleanu D, Rezapour S, Saberpour Z. On fractional integro-differential inclusions via the extended fractional Caputo-Fabrizio derivation. Bound Value Probl. 2019;2019:1–79.
  • Cernea A. On some fractional differential inclusions with random parameters. Fract Calculus Appl Anal. 2018;21(21):190–199.
  • Chalishajar DN, Karthikeyan K. Existence and uniqueness results for boundary value problems of higher order fractional integro-differential equations involving Gronwall's inequality in banach spaces. Acta Mathematica Scientia. 2013;33(3):758–772.
  • Kamenskii M, Obukhovskii V, Petrosyan G, Yao JC. Boundary value problems for semilinear differential inclusions of fractional order in a banach space. Appl Anal. 2017;97(4):571–591. Available from https://doi.org/https://doi.org/10.1080/00036811.2016.1277583.
  • Kaura J, Gupta RK, Kumar S. On explicit exact solutions and conservation laws for time fractional variable – coefficient coupled Burger's equations. Commun Nonlinear Sci Numer Simul. 2019;83:105108. Available from https://doi.org/https://doi.org/10.1016/j.cnsns.2019.105108.
  • Rebai H, Seba D. Weak solutions for nonlinear fractional differential equation with fractional separated boundary conditions in banach spaces. Filomat. 2018;32(3):1117–1125.
  • Seba D. Nonlinear fractional differential inclusion with nonlocal fractional integro- differential boundary conditions in banach spaces. Math Bohem. 2017;142(3):1–13.
  • Seba D, Rebai H, Henderson J. Existence result for nonlinear fractional differential equations with nonlocal fractional integro-differential boundary conditions in banach spaces. Georgian Math J. 2019;1–7. Available from https://doi.org/https://doi.org/10.1515/gmj-2019-2009.
  • Sousa J, da Vanterler C, Capelas de Oliveira E. On the ψ-Hilfer fractional derivative. Commun Nonlinear Sci Numer Simul. 2018;60:72–91.
  • Harikrishnan S., Shah K, Baleanu D, et al. Note on the solution of random differential equations via ψ-Hilfer fractional derivative. Adv Differ Equ. 2018;2018(224):1–9.
  • Liu K, Wang JR, O'Regan D. Ulam-Hyers-Mittag-Leffler stability for ψ-Hilfer fractional order delay differential equations. Adv Differ Equ. 2019;2019(50):1–12.
  • Sousa J da Vanterler, Capelas de Oliveira E. Stability of the fractional Volterra integro-differential equation by means of ψ-Hilfer operator. Math Meth Appl Sci. 2019;42:3033–3043.
  • Sugumaran H, Ibrahim RW, Kanagarajan K. On ψ-Hilfer fractional differential equation with complex order. Univ J Math Appl. 2018;1(1):33–38.
  • Ahmad B, Nieto JJ. A study of impulsive fractional differential inclusions with anti-periodic boundary conditions. Fract Differ Calculus. 2012;2(1):1–15.
  • Ahmed HM, El-Borai MM, El-Owaidy HM, et al. Impulsive Hilfer fractional differential equations. Adv Differ Equ. 2018;2018(226):1–20.
  • Gao D, Li J. Existence results for impulsive fractional differential inclusions with two different caputo fractional derivatives. Discrete Dyn Nat Soc. 2019;2019:1–9.
  • Hilal K, Guida K, Ibnelazyz L, et al. Existence results for an impulsive fractional integro-differential equations with a non-compact semigroup. In: Melliani S, Castillo O, editors. Recent advances in intuitionistic fuzzy logic systems. Studies in fuzziness and soft computing, Vol. 372. Cham: Springer; 2019. p. 191–211.
  • Jarad F, Harikrishnan S, Shah K, et al. Existence and stability results to a class of fractional random implicit differential equations involving a generalized Hilfer fractional derivative. Discrete Continuous Dynamical Systems Ser S. 2019;13(3):723–739. Available from https://doi.org/https://doi.org/10.3934/dcdss.2020040.
  • Xie S. Existence results of mild solutions for impulsive fractional integro-differential evolution equations with infinite delay. Fract Calc Appl Anal. 2014;17(4):1158–1174.
  • Aimene D, Baleanu D, Seba D. Controllability of semilinear impulsive Atangana-Baleanu fractional differential equations with delay. Chaos Solitons Fractals. 2019;128:51–57.
  • Aimene D, Seba D, Laoubi K. Controllability of impulsive fractional functional evolution equations with infinite state-dependent delay in banach spaces. Math Meth Appl Sci. 2019;1–16. Available from https://doi.org/https://doi.org/10.1002/mma.5644.
  • Zhou Y, Suganya S, Arjunan MM. Existence and controllability for impulsive evolution inclusions without compactness. J Dyn Control Syst. 2018;24:297–311.
  • Ali A, Shah K, Jarad F, et al. Existence and stability analysis to a coupled system of implicit type impulsive boundary value problems of fractional order differential equations. Adv Differ Equ. 2019;2019(101):1–21.
  • Ntouyas SK, Tariboon J, Thiramanus P. Mixed problems of fractional coupled systems of Riemann–Liouville differential equations and Hadamard integral conditions. J Comput Anal Appl. 2016;21(5):813–828.
  • Rao SN, Alesemi M. On a coupled system of fractional differential equations with nonlocal non-separated boundary conditions. Adv Differ. Equ. 2019;2019(97):1–14.
  • Shah K, Khalil H, Khan RA. Investigation of positive solutions to a coupled system of impulsive boundary value problems for nonlinear fractional order differential equations. Chaos Solitons Fractals. 2015;77:240–246.
  • Yang W. Positive solution to nonzero boundary values problem for a coupled system of nonlinear fractional differential equations. Comput Math Appl. 2012;63:288–297.
  • Zhao K, Huang H. Existence results of nonlocal boundary value problem for a nonlinear fractional differential coupled system involving fractional order impulses. Adv Differ Equ. 2019;2019(36):1–13.
  • Alsaedi A, Baleanu D, Etemad S, et al. On coupled systems of time-fractional differential problems by using a new fractional derivative. J Funct Spaces. 2016;2016:1–8.
  • Jin N, Sun S. Solvability of coupled systems of hybrid fractional differential equations and inclusions. Int J. Dyn Syst Differ Equ. 2018;8(4):296–312.
  • Blouhi T, Ferhat M. Coupled system of second-order stochastic neutral differential inclusions driven by Wiener process and poisson jumps. Differ Equ Dyn Syst. 2019;1–15. Available from https://doi.org/https://doi.org/10.1007/s12591-018-00450-y.
  • Deimling K. Multivalued differential equations. Berlin: Walter de Gruyter; 1992.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.