Journal ArticleDOI
Boundary value problems for differential equations with fractional order and nonlocal conditions
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In this article, sufficient conditions for the existence of solutions for a class of boundary value problems for fractional differential equations involving the Caputo fractional derivative and non-local conditions were established.Abstract:
In this paper, we establish sufficient conditions for the existence of solutions for a class of boundary value problem for fractional differential equations involving the Caputo fractional derivative and nonlocal conditions.read more
Citations
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Journal ArticleDOI
Positive solutions for Dirichlet problems of singular nonlinear fractional differential equations
TL;DR: In this article, the existence of positive solutions for the singular fractional boundary value problem was proved by means of a fixed point theorem on a cone, and the proofs were based on regularization and sequential techniques.
Journal ArticleDOI
Positive solutions to singular boundary value problem for nonlinear fractional differential equation
TL;DR: The existence of positive solutions to the singular boundary value problem for fractional differential equation is considered and a fixed point theorem for the mixed monotone operator is relied on.
Journal ArticleDOI
Existence and uniqueness of solutions to a fractional difference equation with nonlocal conditions
TL;DR: The existence and uniqueness of solution to this problem are proved by using a variety of tools from nonlinear functional analysis including the contraction mapping theorem, the Brouwer theorem, and the Krasnosel'skii theorem.
Journal ArticleDOI
Existence of solutions for a class of fractional boundary value problems via critical point theory
Feng Jiao,Yong Zhou +1 more
TL;DR: By the critical point theory, a new approach is provided to study the existence of solutions to the following fractional boundary value problem: {ddt(12"0D"t^-^@b(u^'(t))+12"tD"T^-#@b (u^’(t)))+@?F(t,u(t)=0,a.e. t@?[0,T],u(0)=u
Journal ArticleDOI
Existence results for fractional boundary value problem via critical point theory
Feng Jiao,Yong Zhou +1 more
TL;DR: By the critical point theory, the boundary value problem is discussed for a fractional differential equation containing the left and right fractional derivative operators, and various criteria on the existence of solutions are obtained.
References
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Book
Fractional Integrals and Derivatives: Theory and Applications
TL;DR: Fractional integrals and derivatives on an interval fractional integral integrals on the real axis and half-axis further properties of fractional integral and derivatives, and derivatives of functions of many variables applications to integral equations of the first kind with power and power-logarithmic kernels integral equations with special function kernels applications to differential equations as discussed by the authors.
Book
Applications Of Fractional Calculus In Physics
TL;DR: An introduction to fractional calculus can be found in this paper, where Butzer et al. present a discussion of fractional fractional derivatives, derivatives and fractal time series.
Journal ArticleDOI
Analysis of Fractional Differential Equations
Kai Diethelm,Neville J. Ford +1 more
TL;DR: In this paper, the authors discuss existence, uniqueness, and structural stability of solutions of nonlinear differential equations of fractional order, and investigate the dependence of the solution on the order of the differential equation and on the initial condition.
BookDOI
Fractals and fractional calculus in continuum mechanics
TL;DR: Panagiotopoulos, O.K.Carpinteri, B. Chiaia, R. Gorenflo, F. Mainardi, and R. Lenormand as mentioned in this paper.