Hyers-Ulam stability for nonlocal fractional partial integro-differential equation with uncertainty

Ahmadian, 2017, Fractional differential systems: A fuzzy solution based on operational matrix of shifted Chebyshev polynomials and its applications, IEEE Tran Fuzzy Syst, 25, 218, 10.1109/TFUZZ.2016.2554156

Allahviranloo, 2012, Explicit solutions of fractional differential equations with uncertainty, Soft Comput, 16, 297, 10.1007/s00500-011-0743-y

Amini-Harandi, 2010, A fixed point theorem for contraction type maps in partially ordered metric spaces and application to ordinary differential equations, Nonlinear Anal (TMA), 72, 2238, 10.1016/j.na.2009.10.023

An T.V. , Vu H. and Hoa N.V. , Applications of contractive-like mapping principles to interval-valued fractional integrodifferential equations, J Fixed Point Theory Appl (2017). Doi.org/10.1007/s11784-017-0444-y

Agarwal, 2010, On the concept of solution for fractional differential equations with uncertainty, Nonlinear Anal (TMA), 72, 2859, 10.1016/j.na.2009.11.029

Agarwal, 2012, Fuzzy fractional integral equations under compactness type condition, Fract Calc Appl Anal, 15, 572, 10.2478/s13540-012-0040-1

Balachandran, 2011, On fractional impulsive equations of Sobolev type with nonlocal condition in Banach spaces, Comput Math Appl, 62, 1157, 10.1016/j.camwa.2011.03.031

Chakraverty S. , Tapaswini S. and Behera D. , Fuzzy Arbitrary Order System: Fuzzy Fractional Differential Equations and Applications, Wiley, 2016.

Petrusel, 2013, Vector-valued metrics, fixed points and coupled fixed points for nonlinear operators, Fixed Point Theo Appl, 2013, 218, 10.1186/1687-1812-2013-218

Bede, 2013, Generalized differentiability of fuzzy-valued functions, Fuzzy Sets Syst, 230, 119, 10.1016/j.fss.2012.10.003

Byszewski, 1991, Theorem about the existence and uniqueness of a solution of a nonlocal abstract Cauchy problem in a Banach space, Appl Anal, 40, 11, 10.1080/00036819008839989

Byszewski, 1991, Theorems about existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem, J Math Anal Appl, 162, 494, 10.1016/0022-247X(91)90164-U

Hai, 2016, Generalized differentiability for ndimensional fuzzy-number-valued functions and fuzzy optimization, Inf Sci, 374, 151, 10.1016/j.ins.2016.09.028

Harjani, 2010, Generalized contractions in partially ordered metric spaces and applications to ordinary differential equations, Nonlinear Anal (TMA), 72, 1188, 10.1016/j.na.2009.08.003

Jurja, 2008, Perov type fixed point theorem in generalized ordered metric spaces, Creative Math Inf, 17, 427

Long, 2015, Global existence of solutions to fuzzy partial hyperbolic functional differential equations with generalized Hukuhara derivatives, J Intell Fuzzy Syst, 29, 939, 10.3233/IFS-151623

Long, 2017, Fuzzy fractional partial differential equations in partially ordered metric spaces, Iran J Fuzzy Syst, 14, 107

Long, 2017, The solvability of fuzzy fractional partial differential equations under Caputo gH-differentiability, Fuzzy Sets Syst, 309, 35, 10.1016/j.fss.2016.06.018

Long, 2017, Ulam stability for fractional partial integro-differential equation with uncertainty, Acta Math Vietnam, 42, 675, 10.1007/s40306-017-0207-2

Long H.V. , Nieto J.J. and Son N.T.K. , New approach for studying nonlocal problems related to differential systems and partial differential equations in generalized fuzzy metric spaces, Fuzzy Sets Syst (2017). DOI. 10.1016/j.fss.2016.11.008

Long H.V. , Son N.T.K. and Rodríguez-López R. , Some generalizations of fixed point theorems in partially ordered metric spaces and applications to partial differential equations with uncertainty, Vietnam J Math (2017). DOI. 10.1007/s10013-017-0254-y

Long H.V. , On random fuzzy fractional partial integro-differential equations under Caputo generalized Hukuhara differentiability, Comput Appl Math (2017). DOI. 10.1007/s40314-017-0478-1

Mazandarani, 2013, Modified fractional Euler method for solving fuzzy fractional initial value problem, Commun Nonlinear Sci Numer Simulat, 18, 12, 10.1016/j.cnsns.2012.06.008

Nieto, 2006, Applications of contractive-like mapping principles to fuzzy equations, Rev Mat Complut, 19, 361, 10.5209/rev_REMA.2006.v19.n2.16599

Rezapour, 2011, Some fixed point results for multivalued operators in generalized metric spaces, Comput Math Appl, 61, 2661, 10.1016/j.camwa.2011.03.014

Octavia, 2014, Implicit first order differential systems with nonlocal conditions, Electron J Qual Theo, 69, 1

Octavia, 2001, On the nonlocal initial value problem for first order differential systems, Stud Univ Babes-Bolyai Math, 56, 113

Perov, 1964, On the Cauchy problem for a system of ordinary differential equations, Pviblizhen Met Reshen Differ Uvavn, 2, 115

Precup, 2002, Methods in Nonlinear Integral Equations, 10.1007/978-94-015-9986-3

Precup, 2009, The role of matrices that are convergent to zero in the study of semilinear operator systems, Math Comp Modelling, 49, 703, 10.1016/j.mcm.2008.04.006

Salahshour, 2015, On analytical solutions of the fractional differential equation with uncertainty: Application to the Basset Problem, Entropy, 17, 885, 10.3390/e17020885

Salahshour, 2017, Afractional derivative with non-singular kernel for intervalvalued functions under uncertainty, Optik-Inter J Light Electr Optics, 130, 273, 10.1016/j.ijleo.2016.10.044

Villamizar-Roa, 2015, Existence of solutions to fuzzy differential equations with generalized Hukuhara derivative via contractivelike mapping principles, Fuzzy Sets Syst, 265, 24, 10.1016/j.fss.2014.07.015

Zhou, 2010, Nonlocal Cauchy problem for fractional evolution equations, Nonlinear Anal (RWA), 11, 4465, 10.1016/j.nonrwa.2010.05.029