[PDF] Top 20 Iterative Technology in a Singular Fractional Boundary Value Problem with q Difference

... The q-difference calculus or quantum calculus is an old subject and is rich in history and in ...tional boundary value problem with q-difference (see [1]-[4] and the ... See full document

... or q-difference calculus that can describe many phenomena in various fields of science and ...of q-difference calculus can be found in the book []. For the fractional q-difference cal- culus ... See full document

... This paper is organized as follows. In the next section, we present some definitions and basic lemmas. In Sect. 3, we prove the existence of solutions of the boundary value problem (1.5)–(1.6) by ... 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

... Setting Q(x) = (x/) + , V(x) = (x/) + (/), p ∗ = /, and β = , there exists a constant M ∗ > . satisfying (.). Thus, the hypothesis of Theorem . is satisfied. In consequence, the ... See full document

... , fractional q-difference equations have gained considerable popularity and importance due to the fact that they can describe the natural phenomena and the math- ematical model more ...for ... See full document

... be singular at u = . Since finding positive solutions of boundary value problems is interest in various fields of sciences, fractional q-calculus equations has tremendous potential for ... See full document

... considering fractional q-difference equa- tions on the ...following boundary value problem of nonlinear fractional q-difference equations on the ... See full document

... In this paper, we investigate the existence and uniqueness of solutions for mixed fractional q-difference boundary value problems involving the Riemann–Liouville and the Caputo ... See full document

... Since k ∈ (, ) by assumption (.), therefore, F is a contraction. Hence, it follows by Banach’s contraction principle that the problem (.)-(.) has a unique solution. In case L(t) = L (L is a constant), the ... See full document

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

... where 1 < α ≤ 2 is a real number, f : 0, 1 × 0, ∞ → 0, ∞ is continuous and D α 0 is the fractional derivative in the sense of Riemann-Liouville. Recently, Qiu and Bai 9 have proved the existence of a positive ... 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. Several ... See full document

... the singular coupled integral boundary value problem of nonlinear higher-order fractional q-difference ...the problem are ... See full document

... Al-Askar, “On the Existence of Positive Solutions for a Boundary Value Problem of Fracntional Order,” International Journal of Mathematical Analysis, Vol.. Lü, “Positive Solutions for Bo[r] ... See full document

... The q-difference equations initiated in the beginning of the th century [–], is a very interesting field in difference ...on q-difference equations, we refer the reader to ...of boundary value ... See full document

... for q-derivatives. So boundary value problems for fractional q-difference equations have become of importance and the existence of positive solutions has been studied by a great number ... See full document

... of singular fractional differential system with integral boundary conditions is considered in this paper and many types of equation system are contained in this equation system because there are many ... See full document

... The rest of the paper is organized as follows. In Section  we briefly give some basic nota- tions, definitions and lemmas. In Section  we collect some auxiliary results needed in the proofs of our main results. Section  ... See full document