Existence results for fractional differential systems through a local minimization principle

In this paper, we investigate the existence of one weak solution for a class of fractional differential systems. The approach is based on variational methods for smooth functionals defined on reflexive Banach spaces. The main result is also demonstrated with examples.

[1]  Yong Zhou,et al.  Controllability for fractional evolution inclusions without compactness , 2015 .

[2]  Yong Zhou,et al.  Existence Results for fractional boundary Value Problem via Critical Point Theory , 2012, Int. J. Bifurc. Chaos.

[3]  Marek Galewski,et al.  Existence results for one‐dimensional fractional equations , 2014, 1402.1529.

[4]  J. A. Tenreiro Machado,et al.  Nonlinear dynamics for local fractional Burgers’ equation arising in fractal flow , 2016 .

[5]  N. Ford,et al.  Analysis of Fractional Differential Equations , 2002 .

[6]  Xinwei Su,et al.  Boundary value problem for a coupled system of nonlinear fractional differential equations , 2009, Appl. Math. Lett..

[7]  L. Kong,et al.  Positive solutions for a semipositone fractional boundary value problem with a forcing term , 2011 .

[8]  Biagio Ricceri A general variational principle and some of its applications , 2000 .

[9]  Yong Zhou,et al.  A class of fractional evolution equations and optimal controls , 2011 .

[10]  Bashir Ahmad,et al.  On four-point nonlocal boundary value problems of nonlinear integro-differential equations of fractional order , 2010, Appl. Math. Comput..

[11]  Yong Zhou,et al.  Fractional Evolution Equations and Inclusions: Analysis and Control , 2016 .

[12]  Yong Zhou,et al.  On the time-fractional Navier-Stokes equations , 2017, Comput. Math. Appl..

[13]  Giovanni Molica Bisci,et al.  Some remarks for one-dimensional mean curvature problems through a local minimization principle , 2013 .

[14]  H. Srivastava,et al.  Theory and Applications of Fractional Differential Equations , 2006 .

[15]  Yulin Zhao,et al.  Infinitely many solutions for fractional differential system via variational method , 2016 .

[16]  Yong Zhou,et al.  Existence of mild solutions for fractional evolution equations , 2013 .

[17]  Yong Zhou,et al.  Existence of solutions for a class of fractional boundary value problems via critical point theory , 2011, Comput. Math. Appl..

[18]  Yong Zhou,et al.  Abstract Cauchy problem for fractional functional differential equations , 2013 .

[19]  Yonghong Wu,et al.  Variational structure and multiple solutions for a fractional advection-dispersion equation , 2014, Comput. Math. Appl..

[20]  Yong Zhou Basic Theory of Fractional Differential Equations , 2014 .

[21]  Yong Zhou,et al.  On the concept and existence of solution for impulsive fractional differential equations , 2012 .

[22]  Xiping Liu,et al.  Multiplicity of solutions for integral boundary value problems of fractional differential equations with upper and lower solutions , 2014, Appl. Math. Comput..

[23]  Agnieszka B. Malinowska,et al.  Variational Methods for the Fractional Sturm--Liouville Problem , 2013, 1304.6258.

[24]  Jing Chen,et al.  Existence and Multiplicity of Solutions for Some Fractional Boundary Value Problem via Critical Point Theory , 2012 .

[25]  Xingqiu Zhang,et al.  Existence of positive solutions for the singular fractional differential equations , 2013 .

[26]  H. Srivastava,et al.  Local Fractional Integral Transforms and Their Applications , 2015 .

[27]  Xinhong Zhang,et al.  Asymptotic behavior of stochastic Gilpin-Ayala mutualism model with jumps , 2013 .