Quasilinearization for fractional differential equations of riemann-liouville type

In this paper, we deal with the quasilinearization for Riemann-Liouville fractional differential equations with two point boundary condition. By establishing a new comparison principle we get a monotone sequence which converges quadratically to the unique solution of the fractional differential equations. 2010 Mathematics Subject Classification: 26A33; 93C15

[1]  W. Marsden.  I and J , 2012 .

[2]  A. El-Sayed,et al.  Existence results for nonlinear quadratic functional integral equations of fractional orders , 2013 .

[3]  Jinrong Wang,et al.  Nonlocal Cauchy problems for fractional evolution equations involving Volterra-Fredholm type integral operators , 2012 .

[4]  Zhenhai Liu,et al.  Relaxation in nonconvex optimal control problems described by fractional differential equations , 2014 .

[5]  J. Vasundhara Devi,et al.  Generalized quasilinearization for fractional differential equations , 2010, Comput. Math. Appl..

[6]  Rabha W. Ibrahim,et al.  Global controllability of a set of fractional differential equations , 2011 .

[7]  T. Kaczorek,et al.  Fractional Differential Equations , 2015 .

[8]  O. Agrawal,et al.  Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering , 2007 .

[9]  Xiuwen Li,et al.  Controllability of nonlinear fractional impulsive evolution systems , 2013 .

[10]  M. Benchohra,et al.  Boundary value problems for differential equations with fractional order and nonlocal conditions , 2009 .

[11]  V. Lakshmikantham,et al.  Generalized Quasilinearization for Nonlinear Problems , 1998 .

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

[13]  Xiuwen Li,et al.  On the Controllability of Impulsive Fractional Evolution Inclusions in Banach Spaces , 2013, J. Optim. Theory Appl..

[14]  V. Lakshmikantham,et al.  Theory of Fractional Dynamic Systems , 2009 .

[15]  A. Rontó,et al.  Periodic successive approximations and interval halving , 2012 .

[16]  Kevin Barraclough,et al.  I and i , 2001, BMJ : British Medical Journal.

[17]  Miklós Rontó,et al.  On the parametrization of boundary-value problems with three-point non-linear restrictions , 2012 .

[18]  Wenyong Zhong,et al.  Computers and Mathematics with Applications Nonlocal and Multiple-point Boundary Value Problem for Fractional Differential Equations , 2022 .

[19]  Alberto Cabada,et al.  Existence results and the monotone iterative technique for systems of nonlinear fractional differential equations , 2012, Appl. Math. Lett..