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On the “bang-bang” principle for a class of Riemann-Liouville fractional semilinear evolution inclusions

  • Zhenhai Liu EMAIL logo , Maojun Bin and Xiaoyou Liu
Published/Copyright: December 30, 2016
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Mathematica Slovaca
From the journal Mathematica Slovaca Volume 66 Issue 6

Abstract

In this paper, we research the existence of solutions for a class of Riemann-Liouville fractional evolution inclusions with nonconvex right hand side. Our main results obtain the existence of the extreme solution and the relationship of the solution sets between the original problem and the convexified problem. In the end, we give an example to illustrate the applications of the abstract results.

MSC 2010: Primary 35R11; Secondary 47H04
Keywords: fractional evolution inclusions; Riemann-Liouville fractional derivative; C1 − α-mild solution; “bangbang” principle

(Communicated by Michal Fečkan)

Funding statement: This work was supported by NNSF of China Grant No. 11671101 and Special Funds of Guangxi Distinguished Experts Construction Engineering

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Received: 2013-8-28
Accepted: 2014-10-13
Published Online: 2016-12-30
Published in Print: 2016-12-1

© 2016 Mathematical Institute Slovak Academy of Sciences

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https://doi.org/10.1515/ms-2016-0226
Keywords for this article
fractional evolution inclusions; Riemann-Liouville fractional derivative; C1 − α-mild solution; “bangbang” principle

Articles in the same Issue

  2. A triple representation of lattice effect algebras
  4. Periods of morgan-voyce sequences and elliptic curves
  6. Multiplicative generalized derivations on ideals in semiprime rings
  8. A few remarks on Poincaré-Perron solutions and regularly varying solutions
  10. Applications of extremal theorem and radius equation for a class of analytic functions
  12. On the “bang-bang” principle for a class of Riemann-Liouville fractional semilinear evolution inclusions
  14. New criteria for global exponential stability of linear time-varying volterra difference equations
  16. On approximation of functions by some hump matrix means of Fourier series
  18. Pseudo-amenability and pseudo-contractibility for certain products of Banach algebras
  20. Poisson kernels on semi-direct products of abelian groups
  22. Locally convex projective limit cones
  24. On the properties (wL) and (wV)
  26. On the existence of solutions for quadratic integral equations in Orlicz spaces
  28. Existence and uniqueness of best proximity points under rational contractivity conditions
  30. Almost Weyl structures on null geometry in indefinite Kenmotsu manifolds
  32. On the internal approach to differential equations 3. Infinitesimal symmetries
  34. A Characterization of the discontinuity point set of strongly separately continuous functions on products
  36. Wick differential and Poisson equations associated to the 𝚀𝚆𝙽-Euler operator acting on generalized operators
  38. Multivariate EIV models
  40. On codes over 𝓡k, m and constructions for new binary self-dual codes
  42. Domination number of total graphs
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