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On the concept of solution for fractional differential equations with uncertainty. (English) Zbl 1188.34005
Summary: We consider a differential equation of fractional order with uncertainty and present the concept of solution. It extends, for example, the cases of first order ordinary differential equations and of differential equations with uncertainty. Some examples are presented.

MSC:
34A08 Fractional ordinary differential equations and fractional differential inclusions
34A07 Fuzzy ordinary differential equations
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[1] Kilbas, A.A.; Srivastava, H.M.; Trujillo, J.J., Theory and applications of fractional differential equations, (2006), Elsevier Science B.V Amsterdam · Zbl 1092.45003
[2] Kiryakova, V., Generalized fractional calculus and applications, (1994), Longman Scientific & Technical Harlow, copublished in the United States with John Wiley & Sons, Inc., New York · Zbl 0882.26003
[3] Lakshmikantham, V.; Vatsala, A.S., Basic theory of fractional differential equations, Nonlinear anal., 69, 2677-2682, (2008) · Zbl 1161.34001
[4] Miller, K.S.; Ross, B., An introduction to the fractional calculus and differential equations, (1993), John Wiley New York · Zbl 0789.26002
[5] Podlubny, I., Fractional differential equation, (1999), Academic Press San Diego · Zbl 0893.65051
[6] Ahmad, B.; Nieto, J.J., Existence results for a coupled system of nonlinear fractional differential equations with three-point boundary conditions, Comput. math. appl., 58, 1838-1843, (2009) · Zbl 1205.34003
[7] Araya, D.; Lizama, C., Almost automorphic mild solutions to fractional differential equations, Nonlinear anal., 69, 3692-3705, (2008) · Zbl 1166.34033
[8] Bonilla, B.; Rivero, M.; Rodríguez-Germá, L.; Trujillo, J.J., Fractional differential equations as alternative models to nonlinear differential equations, Appl. math. comput., 187, 79-88, (2007) · Zbl 1120.34323
[9] Chang, Y.-K.; Nieto, J.J., Some new existence results for fractional differential inclusions with boundary conditions, Math. comput. modelling, 49, 605-609, (2009) · Zbl 1165.34313
[10] Diethelm, K.; Ford, N.J., Analysis of fractional differential equations, J. math. anal. appl., 265, 229-248, (2002) · Zbl 1014.34003
[11] Shuqin, Z., Monotone iterative method for initial value problem involving riemann – liouville fractional derivatives, Nonlinear anal., 71, 2087-2093, (2009) · Zbl 1172.26307
[12] Lakshmikantham, V.; Leela, S.; Vasundhara Devi, J., Theory of fractional dynamic systems, (2009), Cambridge Scientific Pub Cambridge, UK · Zbl 1188.37002
[13] Laksmikantham, V.; Leela, S., Nagumo-type uniqueness result for fractional differential equations, Nonlinear anal., 8, 2886-2889, (2009) · Zbl 1177.34003
[14] Belmekki, M.; Nieto, J.J.; Rodríguez-López, R., Existence of periodic solutions for a nonlinear fractional differential equation, Bound. value probl., 2009, (2009), Art. ID. 324561 · Zbl 1181.34006
[15] iamond, P.D; Kloeden, P.E., Metric spaces of fuzzy sets, (1994), World Scientific Singapore
[16] Lakshmikantham, V.; Mohapatra, R.N., Theory of fuzzy differential equations and applications, (2003), Taylor & Francis London · Zbl 0997.34051
[17] Nieto, J.J.; Rodríguez-López, R.; Georgiou, D.N., Fuzzy differential systems under generalized metric spaces approach, Dynam. systems appl., 17, 1-24, (2008) · Zbl 1168.34005
[18] Nieto, J.J.; Rodríguez-López, R.; Franco, D., Linear first-order fuzzy differential equation, Int. J. uncertain. fuzziness knowl. based syst. l., 14, 687-709, (2006) · Zbl 1116.34005
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