Nonexistence of Global Solutions to Higher-Order Time-Fractional Evolution Inequalities with Subcritical Degeneracy

Agarwal, Ravi P.; Alhumayan, Soha Mohammad; Jleli, Mohamed; Samet, Bessem

doi:10.3390/math9212765

Cited by 1 publication

(1 citation statement)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This observation motivated the study of fractional partial differential equations in various directions. In particular, several studies related to the nonexistence of solutions have been conducted (see, e.g., [11][12][13][14][15][16][17] and the references therein). For instance, in [11], the authors extended some of the obtained results in [6] to the fractional case.…”

Section: Introductionmentioning

confidence: 99%

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

Alshabanat,

Almoalim,

Jleli

et al. 2023

Axioms

Self Cite

View full text Add to dashboard Cite

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.

show abstract