On the Existence and Uniqueness for High Order Fuzzy Fractional Differential Equations with Uncertainty

A class fuzzy fractional differential equation (FFDE) involving Riemann-Liouville H-differentiability of arbitrary order q>1 is considered. Using Krasnoselskii-Krein type conditions, Kooi type conditions, and Rogers conditions we establish the uniqueness and existence of the solution after determining the equivalent integral form of the solution.

[1]  P. Agarwal,et al.  The general solution for impulsive differential equations with Riemann-Liouville fractional-order q ∈ (1,2) , 2015 .

[2]  T. Bhaskar,et al.  New uniqueness results for fractional differential equations , 2013 .

[3]  Marek T. Malinowski,et al.  Random fuzzy fractional integral equations - theoretical foundations , 2015, Fuzzy Sets Syst..

[4]  Tofigh Allahviranloo,et al.  Fuzzy Laplace transforms , 2009, Soft Comput..

[5]  Weiyin Fei,et al.  Existence and uniqueness of solution for fuzzy random differential equations with non-Lipschitz coefficients , 2007, Inf. Sci..

[6]  S. Salahshour,et al.  Tau method for the numerical solution of a fuzzy fractional kinetic model and its application to the oil palm frond as a promising source of xylose , 2015, J. Comput. Phys..

[7]  V. Lakshmikantham,et al.  A Krasnoselskii–Krein-type uniqueness result for fractional differential equations , 2009 .

[8]  Ngo Van Hoa,et al.  Fuzzy functional integro-differential equations under generalized H-differentiability , 2014, J. Intell. Fuzzy Syst..

[9]  Francesco Mainardi,et al.  Fractional Calculus: Some Basic Problems in Continuum and Statistical Mechanics , 2012, 1201.0863.

[10]  Guotao Wang,et al.  On some new integral inequalities of Gronwall–Bellman–Bihari type with delay for discontinuous functions and their applications , 2016 .

[11]  Praveen Agarwal,et al.  New concepts of fractional quantum calculus and applications to impulsive fractional q-difference equations , 2015 .

[12]  Junmi Li,et al.  Stability analysis of fractional order systems based on T–S fuzzy model with the fractional order $$\alpha : 0<\alpha <1$$α:0 , 2014 .

[13]  M. Benchohra,et al.  FUZZY SOLUTIONS FOR IMPULSIVE DIFFERENTIAL EQUATIONS , 2007 .

[14]  Dumitru Baleanu,et al.  On Fuzzy Fractional Laplace Transformation , 2014 .

[15]  V. Lakshmikantham,et al.  Nagumo-type uniqueness result for fractional differential equations , 2009 .

[16]  Ngo Van Hoa,et al.  Fuzzy fractional functional differential equations under Caputo gH-differentiability , 2015, Commun. Nonlinear Sci. Numer. Simul..

[17]  Fariba Bahrami,et al.  Existence of global solutions to nonlinear fuzzy Volterra integro-differential equations , 2012 .

[18]  Tofigh Allahviranloo,et al.  SOLVING FUZZY FRACTIONAL DIFFERENTIAL EQUATIONS BY FUZZY LAPLACE TRANSFORMS , 2012 .

[19]  L. S. Chadli,et al.  Solving second-order fuzzy differential equations by the fuzzy Laplace transform method , 2015, Advances in Difference Equations.

[20]  Metzler,et al.  Generalized chapman-kolmogorov equation: A unifying approach to the description of anomalous transport in external fields , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[21]  A. Guezane-Lakoud,et al.  Positive solutions for an oscillator fractional initial value problem , 2017 .

[22]  Tofigh Allahviranloo,et al.  Fuzzy fractional differential equations under generalized fuzzy Caputo derivative , 2014, J. Intell. Fuzzy Syst..

[23]  M. T. Malinowski.  Existence theorems for solutions to random fuzzy differential equations , 2010 .

[24]  Tofigh Allahviranloo,et al.  Fuzzy fractional differential equations with Nagumo and Krasnoselskii-Krein condition , 2011, EUSFLAT Conf..

[25]  N. Phu,et al.  Interval-valued functional integro-differential equations , 2014 .

[26]  J. Klafter,et al.  The random walk's guide to anomalous diffusion: a fractional dynamics approach , 2000 .

[27]  Dumitru Baleanu,et al.  On Analytical Solutions of the Fractional Differential Equation with Uncertainty: Application to the Basset Problem , 2015, Entropy.

[28]  Vishwesh A. Vyawahare,et al.  Stability Analysis of Fractional-order Systems , 2012 .

[29]  Positive Solutions of the Fractional Relaxation Equation Using Lower and Upper Solutions , 2016 .

[30]  Alan D. Freed,et al.  On the Solution of Nonlinear Fractional-Order Differential Equations Used in the Modeling of Viscoplasticity , 1999 .

[31]  N. Ford,et al.  A Predictor-Corrector Approach for the Numerical Solution of Fractional Differential Equations , 2013 .

[32]  Tofigh Allahviranloo,et al.  Explicit solutions of fractional differential equations with uncertainty , 2012, Soft Comput..

[33]  Tofigh Allahviranloo,et al.  On Solutions of Linear Fractional Differential Equations with Uncertainty , 2013 .

[34]  Hans-Jürgen Zimmermann,et al.  Fuzzy Set Theory - and Its Applications , 1985 .

[35]  Vasile Lupulescu,et al.  On the fractional differential equations with uncertainty , 2011 .

[36]  V. Lakshmikantham,et al.  Uniqueness and nonuniqueness criteria for ordinary differential equations , 1993 .

[37]  A. Khastan,et al.  New Results on Multiple Solutions for th-Order Fuzzy Differential Equations under Generalized Differentiability , 2009 .

[38]  Yurilev Chalco-Cano,et al.  Calculus for interval-valued functions using generalized Hukuhara derivative and applications , 2013, Fuzzy Sets Syst..

[39]  V. Lupulescu,et al.  FRACTIONAL DIFFERENTIAL EQUATION WITH THE FUZZY INITIAL CONDITION , 2011 .