Evolution fractional differential problems with impulses and nonlocal conditions

Irene Benedetti; Valeri Obukhovskii; Valentina Taddei

doi:10.3934/dcdss.2020149

Article Contents

2020, Volume 13, Issue 7: 1899-1919. Doi: 10.3934/dcdss.2020149

This issue Previous Article A priori estimates for elliptic problems via Liouville type theorems Next Article Positive radial solutions for the Minkowski-curvature equation with Neumann boundary conditions

Evolution fractional differential problems with impulses and nonlocal conditions

1.
Dipartimento di Matematica e Informatica, Università degli Studi di Perugia, I-06123 Perugia, Italy
2.
Faculty of Physics and Mathematics, Voronezh State Pedagogical University, 394043 Voronezh, Russia
3.
Dipartimento di Scienze e Metodi dell'Ingegneria, Università di Modena e Reggio Emilia, I-42122 Reggio Emilia, Italy

^* Corresponding author: Irene Benedetti
^* Corresponding author: Irene Benedetti

Dedicated to Professor Patrizia Pucci on the occasion of her 65th birthday

Received: August 31, 2018

Revised: September 30, 2018

Published: April 2020

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Abstract

We obtain existence results for mild solutions of a fractional differential inclusion subjected to impulses and nonlocal initial conditions. By means of a technique based on the weak topology in connection with the Glicksberg-Ky Fan Fixed Point Theorem we are able to avoid any hypotheses of compactness on the semigroup and on the nonlinear term and at the same time we do not need to assume hypotheses of monotonicity or Lipschitz regularity neither on the nonlinear term, nor on the impulse functions, nor on the nonlocal condition. An application to a fractional diffusion process complete the discussion of the studied problem. 200 words.

Keywords:

Caputo fractional derivative,
impulse functions,
nonlocal initial conditions,
evolution inclusions in abstract spaces.

Mathematics Subject Classification: Primary: 34A08, 34A37, 34B10; Secondary: 34G25.

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References

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