FUZZY FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS IN PARTIALLY ORDERED METRIC SPACES

In this paper, we consider fuzzy fractional partial differential equations under Caputo generalized Hukuhara differentiability. Some new results on the existence and uniqueness of two types of fuzzy solutions are studied via weakly contractive mapping in the partially ordered metric space. Some application examples are presented to illustrate our main results.

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

[2]  J. Harjani,et al.  Generalized contractions in partially ordered metric spaces and applications to ordinary differential equations , 2010 .

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

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

[5]  Fariba Bahrami,et al.  Global solutions of fuzzy integro-differential equations under generalized differentiability by the method of upper and lower solutions , 2015, Inf. Sci..

[6]  Le Hoang Son,et al.  The existence and uniqueness of fuzzy solutions for hyperbolic partial differential equations , 2014, Fuzzy Optim. Decis. Mak..

[7]  Juan J. Nieto,et al.  Applications of Contractive-like Mapping Principles to Fuzzy Equations , 2006 .

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

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

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

[11]  Nguyen Thi Kim Son,et al.  The solvability of fuzzy fractional partial differential equations under Caputo gH-differentiability , 2017, Fuzzy Sets Syst..

[12]  Barnabás Bede,et al.  Generalized differentiability of fuzzy-valued functions , 2013, Fuzzy Sets Syst..

[13]  Nguyen Thi Kim Son,et al.  Global existence of solutions to fuzzy partial hyperbolic functional differential equations with generalized Hukuhara derivatives , 2015, J. Intell. Fuzzy Syst..

[14]  Yurilev Chalco-Cano,et al.  Existence of solutions to fuzzy differential equations with generalized Hukuhara derivative via contractive-like mapping principles , 2015, Fuzzy Sets Syst..

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

[16]  M. Caputo.  Linear Models of Dissipation whose Q is almost Frequency Independent-II , 1967 .

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

[18]  Vu Ho,et al.  On impulsive fuzzy functional differential equations , 2016 .