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Soft Computing

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11.07.2020 | Methodologies and Application

Applications of contractive-like mapping principles to fuzzy fractional integral equations with the kernel \(\psi \)-functions

verfasst von: Ho Vu, Ngo Van Hoa

Erschienen in: Soft Computing | Ausgabe 24/2020

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Abstract

In this work, we present a new class of generalized fractional integral equations with respect to the kernel \(\psi \)-function under the fuzzy concept. The results of this problem can be used to recover a wide class of fuzzy fractional integral equations by the choice of the kernel \(\psi \)-function. Without the Lipschitzian right-hand side, we investigate the existence and uniqueness of the fuzzy solutions by employing the fixed point theorem of weakly contractive mappings in the partially ordered space of fuzzy numbers. The proposed approach is based on the concept of a fuzzy metric space endowed with a partial order and the altering distance functions. In addition, the continuous dependence of solutions on the order and the initial condition of the given problem is also shown. Some concrete examples are presented in order to consolidate the obtained result.

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Agarwal RP, Lakshmikantham V, Nieto JJ (2010) On the concept of solution for fractional differential equations with uncertainty. Nonlinear Anal Theory Methods Appl 72:2859–2862MathSciNetMATH

Agarwal RP, Arshad S, O’Regan D, Lupulescu V (2012) Fuzzy fractional integral equations under compactness type condition. Fract Calc Appl Anal 15:572–590MathSciNetMATH

Ahmadian A, Salahshour S, Chan CS (2017a) Fractional differential systems: a fuzzy solution based on operational matrix of shifted Chebyshev polynomials and its applications. IEEE Trans Fuzzy Syst 25:218–236

Ahmadian A, Ismail F, Salahshour S, Baleanu D, Ghaemi F (2017b) Uncertain viscoelastic models with fractional order: a new spectral tau method to study the numerical simulations of the solution. Commun Nonlinear Sci Numer Simul 53:44–64MathSciNetMATH

Alikhani R, Bahrami F (2013) Global solutions for nonlinear fuzzy fractional integral and integro-differential equations. Commun Nonlinear Sci Numer Simul 18:2007–2017MathSciNetMATH

Allahviranloo T, Salahshour S, Abbasbandy S (2012a) Explicit solutions of fractional differential equations with uncertainty. Soft Comput 16:297–302MATH

Allahviranloo T, Salahshour S, Abbasbandy S (2012b) Solving fuzzy fractional differential equations by fuzzy Laplace transforms. Commun Nonlinear Sci Numer Simul 17:1372–1381MathSciNetMATH

Allahviranloo T, Gouyandeh Z, Armand A (2014) Fuzzy fractional differential equations under generalized fuzzy Caputo derivative. J Intell Fuzzy Syst 26:1481–1490MathSciNetMATH

Almeida R (2017) A Caputo fractional derivative of a function with respect to another function. Commun Nonlinear Sci Numer Simul 44:460–481MathSciNetMATH

An TV, Vu H, Hoa NV (2017a) Applications of contractive-like mapping principles to interval-valued fractional integro-differential equations. J Fixed Point Theory Appl 19:2577–99MathSciNetMATH

An TV, Vu H, Hoa NV (2017) A new technique to solve the initial value problems for fractional fuzzy delay differential equations. Adv Differ Equ 2017:181MathSciNetMATH

Arshad S, Lupulescu V (2011) On the fractional differential equations with uncertainty. Nonlinear Anal Theory Appl 7:85–93MATH

Bede B, Gal SG (2005) Generalizations of the differentiability of fuzzy-number-valued functions with applications to fuzzy differential equations. Fuzzy Sets Syst 151:581–599MathSciNetMATH

Bede B, Stefanini L (2013) Generalized differentiability of fuzzy-valued functions. Fuzzy Sets Syst 230:119–141MathSciNetMATH

Fard OS, Salehi M (2014) A survey on fuzzy fractional variational problems. J Comput Appl Math 271:71–82MathSciNetMATH

Harjani J, Sadarangani K (2010) Generalized contractions in partially ordered metric spaces and applications to ordinary differential equations. Nonlinear Anal 72:1188–1197MathSciNetMATH

Hoa NV (2015a) Fuzzy fractional functional integral and differential equations. Fuzzy Sets Syst 280:58–90MathSciNetMATH

Hoa NV (2015b) Fuzzy fractional functional differential equations under Caputo gH-differentiability. Commun Nonlinear Sci Numer Simul 22:1134–1157MathSciNetMATH

Hoa NV (2020) On the initial value problem for fuzzy differential equations of non-integer order \(\alpha \in (1, 2) \). Soft Comput 24(2):935–954MATH

Hoa NV, Ho V (2019) A survey on the initial value problems of fuzzy implicit fractional differential equations. Fuzzy Sets Syst. https://doi.org/10.1016/j.fss.2019.10.012CrossRef

Hoa NV, Lupulescu V, O’Regan D (2017) Solving interval-valued fractional initial value problem under Caputo gH-fractional differentiability. Fuzzy Sets Syst 309:1–34MathSciNetMATH

Hoa NV, Lupulescu V, O’Regan D (2018) A note on initial value problems for fractional fuzzy differential equations. Fuzzy Sets Syst 347:54–69MathSciNetMATH

Hoa NV, Vu H, Duc TM (2019) Fuzzy fractional differential equations under Caputo–Katugampola fractional derivative approach. Fuzzy Sets Syst 375:70–99MathSciNetMATH

Khastan A, Nieto JJ, Rodríguez-López R (2014) Fuzzy delay differential equations under generalized differentiability. Inf Sci 275:145–67MathSciNetMATH

Long HV, Son NTK, Hoa NV (2017a) Fuzzy fractional partial differential equations in partially ordered metric spaces. Iran J Fuzzy Syst 14:107–126MathSciNetMATH

Long HV, Son NTK, Tam HTT, Yao JC (2017b) Ulam stability for fractional partial integro-differential equation with uncertainty. Acta Math Vietnam 42:675–700MathSciNetMATH

Long HV, Son NK, Tam HT (2017c) The solvability of fuzzy fractional partial differential equations under Caputo gH-differentiability. Fuzzy Sets Syst 309:35–63MathSciNetMATH

Long HV, Nieto JJ, Son NTK (2018) New approach for studying nonlocal problems related to differential systems and partial differential equations in generalized fuzzy metric spaces. Fuzzy Sets Syst 331:26–46MathSciNetMATH

Lupulescu V (2015) Fractional calculus for interval-valued functions. Fuzzy Sets Syst 265:63–85MathSciNetMATH

Lupulescu V, Hoa NV (2017) Interval Abel integral equation. Soft Comput 21:2777–2784MATH

Malinowski MT (2015) Random fuzzy fractional integral equations-theoretical foundations. Fuzzy Sets Syst 265:39–62MathSciNetMATH

Mazandarani M, Kamyad AV (2013) Modified fractional Euler method for solving fuzzy fractional initial value problem. Commun Nonlinear Sci Numer Simul 18:12–21MathSciNetMATH

Mazandarani M, Najariyan M (2014) Type-2 fuzzy fractional derivatives. Commun Nonlinear Sci Numer Simul 19:2354–2372MathSciNetMATH

Nieto JJ, Rodríguez-López R (2005) Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations. Order 22:223–239MathSciNetMATH

Nieto JJ, Rodríguez-López R (2007) Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations. Acta Math Sin 23:2205–2212MathSciNetMATH

Noeiaghdam Z, Allahviranloo T, Nieto JJ (2019) \(q-\)fractional differential equations with uncertainty. Soft Comput 23:9507–9524MATH

Quang LTQ, Hoa NV, Phu ND, Tung TT (2016) Existence of extremal solutions for interval-valued functional integro-differential equations. J Intell Fuzzy Syst 30:3495–3512MATH

Ran ACM, Reurings MCB (2004) A fixed point theorem in partially ordered sets and some applications to matrix equations. Proc Am Math Soc 132:1435–1443MathSciNetMATH

Rodríguez-López R (2008) Monotone method for fuzzy differential equations. Fuzzy Sets Syst 159:2047–76MathSciNetMATH

Salahshour S, Allahviranloo T, Abbasbandy S (2012) Solving fuzzy fractional differentialequations by fuzzy Laplace transforms. Commun Nonlinear Sci Numer Simul 17:1372–1381MathSciNetMATH

Salahshour S, Ahmadian A, Senu N, Baleanu D, Agarwal P (2015) On analytical solutions of the fractional differential equation with uncertainty: application to the Basset problem. Entropy 17:885–902MathSciNetMATH

Sousa JVC, de Oliveira EC (2019) A Gronwall inequality and the Cauchy-type problem by means of \(\psi \)-Hilfer operator. Differ Equ Appl 11:87–106MathSciNetMATH

Stefanini L (2010) A generalization of Hukuhara difference and division for interval and fuzzy arithmetic. Fuzzy Sets Syst 161:1564–1584MathSciNetMATH

Villamizar-Roa EJ, Angulo-Castillo V, Chalco-Cano Y (2015) Existence of solutions to fuzzy differential equations with generalized Hukuhara derivative via contractive-like mapping principles. Fuzzy Sets Syst 265:24–38MathSciNetMATH

Vu H, An TV, Van Hoa N (2020) Ulam-Hyers stability of uncertain functional differential equation in fuzzy setting with Caputo-Hadamard fractional derivative concept. J Intell Fuzzy Syst 38(2):2245–2259. https://doi.org/10.3233/JIFS-191025CrossRef

Titel: Applications of contractive-like mapping principles to fuzzy fractional integral equations with the kernel -functions
verfasst von: Ho Vu
Ngo Van Hoa
Publikationsdatum: 11.07.2020
Verlag: Springer Berlin Heidelberg
Erschienen in: Soft Computing / Ausgabe 24/2020
Print ISSN: 1432-7643
Elektronische ISSN: 1433-7479
DOI: https://doi.org/10.1007/s00500-020-05115-z

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