A Time-Fractional Differential Inequality of Sobolev Type on an Annulus

Author:

Alshabanat Amal1,Almoalim Eman1,Jleli Mohamed2ORCID,Samet Bessem2

Affiliation:

1. Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, Riyadh 11671, Saudi Arabia

2. Department of Mathematics, College of Science, King Saud University, Riyadh 11451, Saudi Arabia

Abstract

Several phenomena from natural sciences can be described by partial differential equations of Sobolev-type. On the other hand, it was shown that in many cases, the use of fractional derivatives provides a more realistic model than the use of standard derivatives. The goal of this paper is to study the nonexistence of weak solutions to a time-fractional differential inequality of Sobolev-type. Namely, we give sufficient conditions for the nonexistence or equivalently necessary conditions for the existence. Our method makes use of the nonlinear capacity method, which consists in making an appropriate choice of test functions in the weak formulation of the problem. This technique has been employed in previous papers for some classes of time-fractional differential inequalities of Sobolev-type posed on the whole space RN. The originality of this work is that the considered problem is posed on an annulus domain, which leads to some difficulties concerning the choice of adequate test functions.

Funder

Princess Nourah bint Abdulrahman University

Publisher

MDPI AG

Subject

Geometry and Topology,Logic,Mathematical Physics,Algebra and Number Theory,Analysis

Reference22 articles.

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4. The Showalter-Sidorov problem as a phenomena of the Sobolev-type equations;Sviridyuk;Bull. Irkutsk. State Univ. Ser. Math.,2010

5. A problem for the generalized Boussinesq filtration equations;Sviridyuk;Sov. Math.,1989

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