Existence and Continuous Dependence on Initial Data of Solution for Initial Value Problem of Fuzzy Multiterm Fractional Differential Equation

In this paper, the fuzzy multiterm fractional differential equation involving Caputo-type fuzzy fractional derivative of order is considered. The uniqueness of solution is established by using the contraction mapping principle and the existence of solution is obtained by Schauder fixed point theorem.

[1]  Ravi P. Agarwal,et al.  On the concept of solution for fractional differential equations with uncertainty , 2010 .

[2]  S. S. Mansouri,et al.  Existence, uniqueness and stability of fuzzy fractional differential equations with local Lipschitz and linear growth conditions , 2017 .

[3]  Tofigh Allahviranloo,et al.  On fuzzy solutions for heat equation based on generalized Hukuhara differentiability , 2015, Fuzzy Sets Syst..

[4]  Juan J. Nieto,et al.  Fuzzy delay differential equations under generalized differentiability , 2014, Inf. Sci..

[5]  Juan J Nieto,et al.  Schauder fixed-point theorem in semilinear spaces and its application to fractional differential equations with uncertainty , 2014 .

[6]  Tayebeh A. Bidgoli,et al.  On the existence and uniqueness of solutions for fuzzy fractional differential equations , 2017 .

[7]  Ali Vahidian Kamyad,et al.  Modified fractional Euler method for solving Fuzzy Fractional Initial Value Problem , 2013, Commun. Nonlinear Sci. Numer. Simul..

[8]  Minghao Chen,et al.  Fractional Jacobi operational matrix for solving Fuzzy Fractional Differential Equation , 2017, J. Intell. Fuzzy Syst..

[9]  Rosana Rodríguez-López,et al.  Periodic boundary value problems for first-order linear differential equations with uncertainty under generalized differentiability , 2013, Inf. Sci..

[10]  Dumitru Baleanu,et al.  A fractional derivative with non-singular kernel for interval-valued functions under uncertainty , 2017 .

[11]  Dumitru Baleanu,et al.  Uncertain viscoelastic models with fractional order: A new spectral tau method to study the numerical simulations of the solution , 2017, Commun. Nonlinear Sci. Numer. Simul..

[12]  Tofigh Allahviranloo,et al.  Existence and uniqueness results for fractional differential equations with uncertainty , 2012, Advances in Difference Equations.

[13]  Chong Wu,et al.  Application of a spectral method to Fractional Differential Equations under uncertainty , 2018, J. Intell. Fuzzy Syst..

[14]  Chee Seng Chan,et al.  Fractional Differential Systems: A Fuzzy Solution Based on Operational Matrix of Shifted Chebyshev Polynomials and Its Applications , 2017, IEEE Transactions on Fuzzy Systems.

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

[16]  Assia Guezane-Lakoud,et al.  On the Existence and Uniqueness for High Order Fuzzy Fractional Differential Equations with Uncertainty , 2016, Adv. Fuzzy Syst..

[17]  Ngo Van Hoa,et al.  Fuzzy fractional differential equations under Caputo-Katugampola fractional derivative approach , 2019, Fuzzy Sets Syst..

[18]  Vasile Lupulescu,et al.  Fractional calculus for interval-valued functions , 2015, Fuzzy Sets Syst..

[19]  Min Qi,et al.  The Cauchy problem for quaternion fuzzy fractional differential equations , 2015, J. Intell. Fuzzy Syst..

[20]  S. Abbasbandy,et al.  M-fractional derivative under interval uncertainty: Theory, properties and applications , 2018, Chaos, Solitons & Fractals.

[21]  Chee Seng Chan,et al.  FTFBE: A numerical approximation for fuzzy time-fractional Bloch equation , 2014, 2014 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE).

[22]  Juan J. Nieto,et al.  Fuzzy fractional initial value problem , 2015, J. Intell. Fuzzy Syst..

[23]  Hongzhou Wang Monotone iterative method for boundary value problems of fuzzy differential equations , 2016, J. Intell. Fuzzy Syst..

[24]  Donal O'Regan,et al.  A note on initial value problems for fractional fuzzy differential equations , 2017, Fuzzy Sets Syst..

[25]  Ngo Van Hoa,et al.  Fuzzy fractional functional integral and differential equations , 2015, Fuzzy Sets Syst..

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

[27]  S. Salahshour,et al.  Variation of constant formula for the solution of interval differential equations of non-integer order , 2017, The European Physical Journal Special Topics.

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

[29]  Barnabás Bede,et al.  Generalizations of the differentiability of fuzzy-number-valued functions with applications to fuzzy differential equations , 2005, Fuzzy Sets Syst..