A priori estimates for weak solution for a time-fractional nonlinear reaction-diffusion equations with an integral condition

Finite Element Method and numerical study for a super-linear reaction-diffusion problem with integral conditions

“…We suppose that F is derivable continuous function on E ⊂ R n . So for every each initial condition for t0 ∈ I and X0 ∈ E the solution of the system (11) if it exists it is unique.…”

Solvability of Dirichlet Problem For a Fractional Partial Differential equation by using energy inequality and Faedo-Galerkin method

“…The study of existence and uniqueness, periodicity, asymptotic behavior, stability, and methods of analytic and numerical solutions of fractional differential equations have been studied extensively in a large cycle works; Especially, The study of existence and uniqueness of solution of fractional partial differential equations are then proved by the well-known Lax-Milgram theorem, Energy estimate and fixed point theorem. Among them, we only mention here the papers [8][9][10][11][12][13][14][15][16][17][18][19][20][21].…”

Solvability of the Solution of Superlinear Hyperbolic Dirichlet Problem

“…Hormander for the development of pseudo differential calculus (in the early 1970s). The complexity of nonlinearity and challenges in their theoretical study in have attracted a lot of interest from many mathematicians and scientists see [8][9][10][11].…”