Browsing by Author "Chaima, SAAD"

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    On the study of the existence of nontrivial solutions for a parabolic fractional problem
    (20 August 1955 University of Skikda, 2024) Chaima, SAAD; Salim ,HAMIDA
    The fundamental focus of this thesis is to investigate certain type of nonlinear fractional partial differential equations (FPDEs), both elliptic and parabolic in nature. Where we interest in this works under certain assumptions on the nonlinear terms to study the existence of weak solutions to five classes of fractional partial differential equations. We use the technique of the Leray-Schauder degree theory together with the application of Schauder fixed point theorem for demonstrate this. Then, for the uniqueness of weak solutions, we suggest the Banach contraction principle theorem. we also use the Galerkin approach to prove the existence and uniqueness results. The first class is the semilinear fractional elliptic problem involving the distributional Riesz fractional gradient in Bessel potential spaces. The second class is semilinear fractional system involving a nonlocal operator. Therefor, the third class in this thesis focuses on adding the transport term in the nonlinear fractional problem involving the distributional Riesz fractional derivative. Then the primary objective in the forth class is time fractional semilinear equations involving Riemann-Liouville time fractional derivative with fractional Laplacian. Finally, the the last class is the time fractional semilinear equation containing the Riemann-Liouville derivative.