EXISTENCE AND UNIQUENESS RESULT OF SOLUTIONS TO INITIAL VALUE PROBLEMS OF FRACTIONAL DIFFERENTIAL EQUATIONS OF VARIABLE-ORDER

In this work, an initial value problem is discussed for a fractional differential equation of variable-order. By means of some analysis techniques and Arzela-Ascoli theorem, existence result of solution is obtained; Using the upper solutions and lower solutions and monotone iterative method, uniqueness existence results of solutions are obtained.

[1]  Y. Chen,et al.  Variable-order fractional differential operators in anomalous diffusion modeling , 2009 .

[2]  YangQuan Chen,et al.  A Physical experimental study of variable-order fractional integrator and differentiator , 2011 .

[3]  Vahid Johari Majd,et al.  Solution existence for non-autonomous variable-order fractional differential equations , 2012, Math. Comput. Model..

[4]  Bertram Ross,et al.  Fractional integration operator of variable order in the holder spaces Hλ(x) , 1995 .

[5]  Duarte Valério,et al.  Variable-order fractional derivatives and their numerical approximations , 2011, Signal Process..

[6]  Soo-Chang Pei,et al.  An iterative method for the design of variable fractional-order FIR differintegrators , 2009, Signal Process..

[7]  Hongguang Sun,et al.  Synthesis of multifractional Gaussian noises based on variable-order fractional operators , 2011, Signal Process..

[8]  Jong-Jy Shyu,et al.  Iterative design of variable fractional-order IIR differintegrators , 2010, Signal Process..

[9]  Carl F. Lorenzo,et al.  Variable Order and Distributed Order Fractional Operators , 2002 .

[10]  W. Chen,et al.  A comparative study of constant-order and variable-order fractional models in characterizing memory property of systems , 2011 .

[11]  Chien-Cheng Tseng,et al.  Design of variable and adaptive fractional order FIR differentiators , 2006, Signal Process..

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

[13]  Fawang Liu,et al.  Stability and convergence of a new explicit finite-difference approximation for the variable-order nonlinear fractional diffusion equation , 2009, Appl. Math. Comput..

[14]  Chien-Cheng Tseng,et al.  Series expansion design of variable fractional order integrator and differentiator using logarithm , 2008, Signal Process..

[15]  Carl F. Lorenzo,et al.  Fractional System Identification: An Approach Using Continuous Order-Distributions , 1999 .

[16]  Jong-Jy Shyu,et al.  A new structure for the design of wideband variable fractional-order FIR differentiators , 2010, Signal Process..

[17]  Carlos F.M. Coimbra,et al.  Mechanics with variable‐order differential operators , 2003 .