Positive Solution of Singular Fractional Differential Equation in Banach Space
نویسندگان
چکیده
منابع مشابه
Positive Solution of Singular Fractional Differential Equation in Banach Space
Recently, fractional differential equations have been investigated extensively. The motivation for those works rises from both the development of the theory of fractional calculus itself and the applications of such constructions in various sciences such as physics, chemistry, aerodynamics, and electrodynamics of the complex medium. For examples and details, see 1–5 and the references therein. ...
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and Applied Analysis 3 Definition 2.2. The fractional derivative of order q > 0 of a continuous function x : 0, ∞ → R is given by Dx t 1 Γ ( n − q) ( d dt )n∫ t 0 x s t − s q−n 1 ds, 2.2 where n q 1, provided that the right side is pointwise defined on 0,∞ . Lemma 2.3 see 7 . 1 If x ∈ L 0, 1 , ρ > σ > 0, then DIx t Iρ−σx t . 2 If ρ > 0, λ > 0, then Dρtλ−1 Γ λ /Γ λ − ρ tλ−ρ−1. Lemma 2.4 see 12 ....
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1 College of Mathematics and Physics, Chongqing University of Posts and Telecommunications, Chongqing 400065, China 2 Key Laboratory of Network Control & Intelligent Instrument, Chongqing University of Posts and Telecommunications, Ministry of Education, Chongqing 400065, China 3 College of Applied Sciences, Beijing University of Technology, Beijing 100124, China 4 Automation Institute, Chongqi...
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Motivated by Vityuk and Golushkov (2004), using the Schauder Fixed Point Theorem and the Contraction Principle, we consider existence and uniqueness of positive solution of a singular partial fractional differential equation in a Banach space concerning with fractional derivative.
متن کاملOn Positive Solution of Nonlinear Fractional Differential Equation
In this paper, the method of upper and lower solutions and the Schauder fixed point theorem are used to investigate the existence and uniqueness of a positive solution for a class of nonlinear fractional differential equations with non-monotone term. An example is also given to illuminate our results. 2000 MSC: 34B15 • 34B18
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ژورنال
عنوان ژورنال: Journal of Applied Mathematics
سال: 2011
ISSN: 1110-757X,1687-0042
DOI: 10.1155/2011/352341