[PDF] Top 20 Boundary value problems of fractional q-difference equations on the half-line

... the fractional q-difference calculus can be traced back to the works in [4] by Al-salam and ...the fractional differ- ential equations, an interest has been observed in studying boundary ... See full document

... Boundary value problems on half-line occur in various applications such as in the study of the unsteady flow of a gas through semi-infinite porous medium, in analyzing the heat transfer ... See full document

... Recently, boundary value problems of nonlinear fractional q-difference equations have aroused considerable ...for boundary value problems of nonlinear ... See full document

... This paper investigates the positive solutions for the singular coupled integral boundary value problem of nonlinear higher-order fractional q-difference equations. By applying a mixed ... See full document

... all the assumptions of Lemma . are satisfied. So the conclusion of Lemma . implies that the boundary value problem (.)-(.) has at least one solution on [, ]. In the special case when φ(u) ≡ , we ... See full document

... Note that the operator A : U → C is continuous and completely continuous. From the choice of U, there is no u ∈ ∂U such that u = λ Au for some λ ∈ (, ). Consequently, by nonlinear alternative of Leray-Schauder type ... See full document

... where  < q < ,  < α < , f : C((, ), (, ∞ )). They proved the existence of positive so- lutions for boundary value problems by utilizing a fixed-point theorem in cones. ... See full document

... Fractional differential calculus is a discipline to which many researchers are dedicating their time, perhaps because of its demonstrated applications in various fields of science and engineering []. Many ... See full document

... Nonlocal BVPs seem to be more interesting than the local ones not only they are more natural but also because of their numerous applications. Moreover, in the numerical ex- periment, the calculation of the value ... See full document

... PW: Fractional q-calculus on a time ...Initial value problems in discrete fractional ...Two-point boundary value problems for finite fractional difference ... See full document

... the fractional q-difference using a single- derivative (Riemann–Liouville or Caputo derivative), in this paper, we consider the exis- tence and uniqueness of the solution to the fractional ... See full document

... Proof We transform the boundary value problem (.) into a fixed point problem, x = Ax, where the operator A is defined by (.). By using the Banach contraction mapping prin- ciple, we shall show that A has ... See full document

... discrete fractional difference operator based on an infinite ...of fractional difference equations has been studied by several ...discrete fractional calculus were published, which helped to ... See full document

... two-point boundary value problems of a nonlinear fractional q-difference equation with dependence on the first order ...using q-difference ...the boundary value ... See full document

... In the present paper we prove existence and uniqueness results for the impulsive bound- ary value problem (.) by using Banach’s contraction mapping principle and Krasnosel- skii’s fixed-point theorem. The rest of ... See full document

... of boundary value problems for fractional q-integro-difference equations with nonlocal fractional q-integral conditions which have different quantum ...of ... See full document

... for fractional q-difference system ...the fractional q-difference sys- tem ...of fractional q-difference equations when τ ij (t) ≡ t for all i and ... See full document

... nonlocal fractional sum-difference boundary value problem for a Caputo fractional functional difference equation with delay, by using the Schauder fixed point theorem and the Banach contraction ... See full document

... the q-derivative and q-integral were ...Riemann-Liouville fractional q-integral and q-difference on an interval [a, b] were given, and their basic properties were ...initial value ... See full document

... The plan of this paper is as follows. We first give the form of solutions of problem (.), second we prove the existence and uniqueness of a solution to problem (.) by the con- traction mapping theorem and the Brouwer ... See full document