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High-Precision Method for Space-Time-Fractional Klein-Gordon Equation Read chapter Read first chapter

2024 | OriginalPaper | Chapter

Existence and Uniqueness Solutions of Fuzzy Fractional Integration-Differential Problem Under Caputo gH-Differentiability

Authors : S. Melliani, E. Arhrrabi, M. Elomari, L. S. Chadli

Published in: Applied Mathematics and Modelling in Finance, Marketing and Economics

Publisher: Springer Nature Switzerland

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Abstract

This paper is devoted to considering the local existence and uniqueness of fuzzy fractional integration-differential problem under Caputo-type fuzzy fractional derivative employing the contraction principle. Some patterns are presented to describe these results.

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Literature
1.
Agarwal, R.P., Lakshmikantham, V., Nieto, J.J.: On the concept of solution for fractional differential equations with uncertainty. Nonlinear Anal. (TMA) 72, 2859–2862 (2010)MathSciNetCrossRef
2.
Agarwal, R.P., Arshad, S., O’Regan, D., Lupulescu, V.: Fuzzy fractional integral equations under compactness type condition. Fract. Calcul. Appl. Anal. 15, 572–590 (2012)MathSciNetCrossRef
3.
Ahmad, M.Z., Hasan, M.K.: A new approach to incorporate uncertainty into Euler’s method. Appl. Math. Sci. 4, 2509–2520 (2010)MathSciNet
4.
Ahmad, M.Z., Hasan, M.K., Baets, B.D.: Analytical and numerical solutions of fuzzy differential equations. Inf. Sci. 236, 156–167 (2013)MathSciNetCrossRef
5.
6.
Alikhani, R., Bahrami, F.: Global solutions for nonlinear fuzzy fractional integral and integrodifferential equations. Commun. Nonlinear Sci. Numer. Simul. 18, 2007–2017 (2013)MathSciNetCrossRef
7.
Allahviranloo, T., Gouyandeh, Z., Armand, A.: Fuzzy fractional differential equations under generalized fuzzy Caputo derivative. J. Intell. Fuzzy Syst. 26, 1481–1490 (2014)MathSciNetCrossRef
8.
Allahviranloo, T., Salahshour, S., Abbasbandy, S.: Explicit solutions of fractional differential equations with uncertainty. Soft Comput. Found Meth. Appl. 16, 297–302 (2012)
9.
Allahviranloo, T., Abbasbandy, S., Sedaghatfar, O., Darabi, P.: A new method for solving fuzzy Integro-differential equation under generalized differentiability. Neural Comput. Appl. 21, 191–196 (2012)CrossRef
10.
Allahviranloo, T., Kiani, N.A., Motamedi, N.: Solving fuzzy differential equations by differential transformation method. Inf. Sci. 179, 956–966 (2009)MathSciNetCrossRef
11.
Allahviranloo, T., Abbasbandy, S., Salahshour, S., Hakimzadeh, A.: A new method for solving fuzzy linear differential equations. Computing 92, 181–197 (2011)MathSciNetCrossRef
12.
Arshad, S., Lupulescu, V.: On the fractional differential equations with uncertainty. Nonlinear Anal. (TMA) 74, 85–93 (2011)
13.
Bede, B., Gal, S.G.: Generalizations of the differentiability of fuzzy-number-valued functions with applications to fuzzy differential equations. Fuzzy Sets Syst. 151, 581–599 (2005)MathSciNetCrossRef
14.
Bede, B., Rudas, I.J., Bencsik, A.L.: First order linear fuzzy differential equations under generalized differentiability. Inf. Sci. 177, 1648–1662 (2007)MathSciNetCrossRef
15.
Bede, B.: A note on ‘two-point boundary value problems associated with non-linear fuzzy differential equations’. Fuzzy Sets Syst. 157, 986–989 (2006)MathSciNetCrossRef
16.
Bede, B., Tenali, G.B., Lakshmikantham, V.: Perspectives of Fuzzy Initial Value Problems. Commun. Appl. Anal. 11, 339–358 (2007)MathSciNet
17.
Bede, B., Stefanini, L.: Generalized differentiability of fuzzy-valued functions. Fuzzy Sets Syst. 230, 119–141 (2013)MathSciNetCrossRef
18.
Diethelm, K.: The Analysis of Fractional Differential Equations (An Application Oriented Exposition Using Differential Operators of Caputo Type). Lecture Notes in Mathematics. Springer, Berlin, Heidelberg (2004)
19.
Fard, O.S., Salehi, M.: A survey on fuzzy fractional variational problems. J. Comput. Appl. Math. 271, 71–82 (2014)MathSciNetCrossRef
20.
Gasilov, N.A., Fatullayev, A.G., Amrahov, S.E., Khastan, A.: A new approach to fuzzy initial value problem. Soft Comput. 18, 217–225 (2014)CrossRef
21.
Gnana Bhaskar, T., Lakshmikantham, V., Leela, S.: Fractional differential equations with a Krasnoselskii-Krein type condition. Nonlinear Anal.: Hybrid Syst. 3, 734–737 (2009)
22.
Hale, J.K.: Theory of Functional Differential Equations. Springer, New York (1977)
23.
Hoa, N.V., Phu, N.D.: Fuzzy functional integro-differential equations under generalized H-differentiability. J. Intell. Fuzzy Syst. 26, 2073–2085 (2014)MathSciNetCrossRef
24.
Hoa, N.V., Tri, P.V., Dao, T.T.: Some global existence results and stability theorem for fuzzy functional differential equations. J. Intell. Fuzzy Syst. (Inpress)
25.
Hukuhara, M.: Integration des applications mesurables dont la valeur est un compact convex. Funkc. Ekvacioj 10, 205–229 (1967)
26.
27.
Khastan, A., Nieto, J.J.: A boundary value problem for second order fuzzy differential equations. Nonlinear Anal.: Theory Methods Appl. 72, 3583–3593 (2010)MathSciNetCrossRef
28.
Khastan, A., Nieto, J.J., Rodriguez-Lopezez, R.: Variation of constant formula for first order fuzzy differential equations. Fuzzy Sets Syst. 177, 20–33 (2011)MathSciNetCrossRef
29.
Khastan, A., Nieto, J.J., Rodriguez-Lopez, R.: Fuzzy delay differential equations under generalized differentiability. Inform. Sci. 275, 145–167 (2014)MathSciNetCrossRef
30.
31.
Kilbas, A.A., Marzan, S.A.: Cauchy problem for differential equation with Caputo fractional derivative. Fract. Calc. Appl. Anal. 7, 297–321 (2004)MathSciNet
32.
Kilbas, A.A., Srivastava, H.M., Trujillo, J.J.: Theory and applications of fractional differential equations. North-Holland Mathematics Studies, vol. 204. Elsevier, Amsterdam (2006)
33.
Kilbas, A.A., Srivastava, H.M., Trujillo, J.J.: Theory and Applications of Fractional Differential Equations. Elsevier Science B.V, Amsterdam (2006)
34.
Kuang, Y.: Delay Differential Equations with Applications in Population Dynamics. Academic, Boston (1993)
35.
Lakshmikantham, V., Leela, S.: A Krasnoselskii-Krein-type uniqueness result for fractional differential equations. Nonlinear Anal.: TMA 71, 3421–3424 (2009)
36.
Lakshmikantham, V., Mohapatra, R.N.: Theory of Fuzzy Differential Equations and Applications. Taylor and Francis, London (2003)
37.
Lakshmikantham, V.: Theory of fractional functional differential equations. Nonlinear Anal.: Theory Methods Appl. 69, 3337–3343 (2008)MathSciNetCrossRef
38.
Lupulescu, V.: On a class of fuzzy functional differential equations. Fuzzy Sets Syst. 160, 1547–1562 (2009)
39.
Lupulescu, V.: Fractional calculus for interval-valued functions. Fuzzy Set Syst. (accepted) (2013)
40.
Lupulescu, V.: On a class of functional differential equations in Banach spaces. Electr. J. Qual. Theory Diff. Eq. (64), 1–17
41.
Malinowski, M.T.: Random fuzzy differential equations under generalized Lipschitz condition. Nonlinear Anal.: Real World Appl. 13, 860–881 (2012)MathSciNetCrossRef
42.
Malinowski, M.T.: Existence theorems for solutions to random fuzzy differential equations. Nonlinear Anal.: Theory Methods Appl. 73, 1515–1532 (2010)MathSciNetCrossRef
43.
Malinowski, M.T.: Second type Hukuhara differentiable solutions to the delay setvalued differential equations. Appl. Math. Comput. 218, 9427–9437 (2012)MathSciNet
44.
Mazandarani, M., Kamyad, A.V.: Modified fractional Euler method for solving fuzzy fractional initial value problem. Commun. Nonlinear Sci. Numer. Simul. 18, 12–21 (2013)MathSciNetCrossRef
45.
Mazandarani, M., Najariyan, M.: Type-2 fuzzy fractional derivatives. Commun. Nonlinear Sci. Numer. Simul. 19, 2354–72 (2014)MathSciNetCrossRef
46.
Nieto, J.J., Khastan, A., Ivaz, K.: Numerical solution of fuzzy differential equations under generalized differentiability. Nonlinear Anal.: Hybrid Syst. 3, 700–707 (2009)MathSciNet
47.
Odibat, Z.M., Shawagfeh, N.T.: Generalized Taylor’s formula. Appl. Math. Comput. 186, 286–293 (2007)MathSciNet
48.
Odibat, Z.M.: Approximations of fractional integrals and Caputo fractional derivatives. Appl. Math. Comput. 178, 527–533 (2006)MathSciNet
49.
Podlubny, I.: Fractional Differential Equation. Academic, San Diego (1999)
50.
Salahshour, S., Allahviranloo, T., Abbasbandy, S., Baleanu, D.: Existence and uniqueness results for fractional differential equations with uncertainty. Adv. Diff. Eq. 2012, 112 (2012)
51.
Salahshour, S., Allahviranloo, T., Abbasbandy, S.: Solving fuzzy fractional differential equations by fuzzy Laplace transforms. Commun. Nonlinear Sci. Numer. Simul. 17, 1372–1381 (2012)MathSciNetCrossRef
52.
53.
Vu, H., Dong, L.S., Hoa, N.V.: Random fuzzy functional integro-differential equations under generalized Hukuhara differentiability. J. Intell. Fuzzy Syst. 27, 1491–1506 (2014)MathSciNetCrossRef
54.
Vu, H., Hoa, N.V., Phu, N.D.: The local existence of solutions for random fuzzy integrodifferential equations under generalized H-differentiability. J. Intell. Fuzzy Syst. 26, 2701–2717 (2014)CrossRef
Metadata
Title
Existence and Uniqueness Solutions of Fuzzy Fractional Integration-Differential Problem Under Caputo gH-Differentiability
Authors
S. Melliani
E. Arhrrabi
M. Elomari
L. S. Chadli
Copyright Year
2024
Book
Applied Mathematics and Modelling in Finance, Marketing and Economics

Print ISBN: 978-3-031-42846-3

Electronic ISBN: 978-3-031-42847-0

Copyright Year: 2024

DOI
https://doi.org/10.1007/978-3-031-42847-0_9

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