Existence and Uniqueness of the Solution for a Time-Fractional Diffusion Equation with Robin Boundary Condition
نویسنده
چکیده
and Applied Analysis 3 is the fundamental solution of TFDE 3, 7–9 . Here H20 12 is the Fox H-function, which is defined via Mellin-Barnes integral representation H20 12 z : H 20 12 [ z | α, α n/2, 1 , 1, 1 ] 1 2πi ∫ C Γ n/2 s Γ 1 s Γ α αs z−s ds, 2.3 where C is an infinite contour on the complex plane circulating the negative real axis counterclockwise. The volume potential is defined by ( Vφ ) x, t ∫ t
منابع مشابه
Existstence and uniqueness of positive solution for a class of boundary value problem including fractional differential equation
In this paper we investigate a kind of boundary value problem involving a fractional differential equation. We study the existence of positive solutions of the problem that fractional derivative is the Reimann-Liouville fractional derivative. At first the green function is computed then it is proved that the green function is positive. We present necessary and sufficient conditions for existen...
متن کاملExistence and uniqueness of positive and nondecreasing solution for nonlocal fractional boundary value problem
In this article, we verify existence and uniqueness of positive and nondecreasing solution for nonlinear boundary value problem of fractional differential equation in the form $D_{0^{+}}^{alpha}x(t)+f(t,x(t))=0, 0
متن کاملExistence of positive solution to a class of boundary value problems of fractional differential equations
This paper is devoted to the study of establishing sufficient conditions for existence and uniqueness of positive solution to a class of non-linear problems of fractional differential equations. The boundary conditions involved Riemann-Liouville fractional order derivative and integral. Further, the non-linear function $f$ contain fractional order derivative which produce extra complexity. Than...
متن کاملExistence and uniqueness of solution of Schrodinger equation in extended Colombeau algebra
In this paper, we establish the existence and uniqueness result of the linear Schrodinger equation with Marchaud fractional derivative in Colombeau generalized algebra. The purpose of introducing Marchaud fractional derivative is regularizing it in Colombeau sense.
متن کاملExistence and uniqueness of solutions for p-laplacian fractional order boundary value problems
In this paper, we study sufficient conditions for existence and uniqueness of solutions of three point boundary vale problem for p-Laplacian fractional order differential equations. We use Schauder's fixed point theorem for existence of solutions and concavity of the operator for uniqueness of solution. We include some examples to show the applicability of our results.
متن کامل