Existence and Uniqueness Results for Fractional (p, q)-Difference Equations with Separated Boundary Conditions (original) (raw)
Existence and uniqueness results for q-fractional difference equations with p-Laplacian operators
Advances in Difference Equations, 2015
In this paper, we consider the following two-point boundary value problem for q-fractional p-Laplace difference equations. New results on the existence and uniqueness of solutions for q-fractional boundary value problem are obtained. These results extend the corresponding ones of ordinary differential equations of integer order. Finally, an example is presented to illustrate the validity and practicability of our main results.
Existence and uniqueness of solutions to a fractional difference equation with nonlocal conditions
Computers & Mathematics with Applications, 2011
In this paper, we consider a discrete fractional boundary value problem with p-Laplacian operator of the form ⎧ ⎪ ⎨ ⎪ ⎩ β [φ p (α y)](t) + f (α + β + t − 1, y(α + β + t − 1)) = 0, t ∈ [0, b] N 0 , α y(β − 2) = α y(β + b) = 0, y(α + β − 4) = y(α + β + b) = 0, where f : [α +β −4, α +β +b] N α+β−4 ×R → R is a continuous function, and p > 1, 1 < α, β ≤ 2. We study the existence and uniqueness of solution to this problem by using a variety of tools from nonlinear functional analysis including the contraction mapping theorem and Brouwer fixed point theorem.
Existence Results for Nonlinear Fractional Difference Equation
Advances in Difference Equations, 2011
This paper is concerned with the initial value problem to a nonlinear fractional difference equation with the Caputo like difference operator. By means of some fixed point theorems, global and local existence results of solutions are obtained. An example is also provided to illustrate our main result.
Journal of Inequalities and Applications
In this work, a proposed system of fractional boundary value problems is investigated concerning its unbounded solutions’ existence for a class of nonlinear fractional q-difference equations in the context of the Riemann–Liouville fractional q-derivative on an infinite interval. The system’s solution is formulated with the help of Green’s function. A compactness criterion is established in a special space. All the obtained results of uniqueness and existence are investigated with the help of fixed-point theorems. Some essential examples are illustrated to support our main outcomes.
Fractal and Fractional
The authors investigate the existence of solutions to a class of boundary value problems for fractional q-difference equations in a Banach space that involves a q-derivative of the Caputo type and nonlinear integral boundary conditions. Their result is based on Mönch’s fixed point theorem and the technique of measures of noncompactness. This approach has proved to be an interesting and useful approach to studying such problems. Some basic concepts from the fractional q-calculus are introduced, including q-derivatives and q-integrals. An example of the main result is included as well as some suggestions for future research.
Existence of positive solutions of nonlinear fractional q-difference equation with parameter
Advances in Difference Equations, 2013
In this paper, we study the boundary value problem of a class of nonlinear fractional q-difference equations with parameter involving the Riemann-Liouville fractional derivative. By means of a fixed point theorem in cones, some positive solutions are obtained. As applications, some examples are presented to illustrate our main results. MSC:39A13, 34B18, 34A08.