Study of certain partial differential equations of fractional order

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dc.contributor.authorBelhad, Tahar
dc.date.accessioned2024-03-13T08:35:07Z
dc.date.available2024-03-13T08:35:07Z
dc.date.issued2023
dc.description.abstractIn this thesis, we study some nonlinear elliptic problems involving rational operators. The difficulty lies in introducing non-classical functional spaces. In the first part, we studied the Dirichlet boundary value problem involving the rational operator p(x, y)−Laplacian. We base the outcome of existence under certain conditions on nonlinearity. Our goal is to apply Berkovits degree theorem to quasi-continuous operators of type (S+) generalized to real reflective Banach spaces. Through this theory, we prove the existence of weak, non-intuitive solutions to this problem. We then study another problem involving Ds, which is the distributive fractional Riesz gradient for 0 < s < 1, as a nonlocal operator generated by an Lèvy operation. Based on the invariance result for pseudotone operators, we have proven that there is at least one weak solution to such a problem. Moreover, we obtain the uniqueness of the solution to the problem under some considerations, and all of this from the theoretical side. From the numerical side, we have used a technique that is a combination of the Elzaki transformation method and the variational iteration method called the Elzaki variational iteration method (EVIM) on nonlinear fractional partial differential equations.
dc.identifier.urihttp://dspace.univ-skikda.dz:4000/handle/123456789/324
dc.language.isoother
dc.publisherUniversity August 20, 1955 –Skikda
dc.titleStudy of certain partial differential equations of fractional order
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