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14.05.2023 | Fuzzy systems and their mathematics

Fuzzy natural transform method for solving fuzzy differential equations

verfasst von: Shabir Ahmad, Aman Ullah, Abd Ullah, Ngo Van Hoa

Erschienen in: Soft Computing | Ausgabe 13/2023

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Abstract

This article establishes a new transform method to seek the solution to some fuzzy differential equations. For the first time in the literature, the fuzzy natural transform method (FNTM) is introduced to solve the integer-order differential equations and non-integer-order differential equations in an uncertain environment. To do this, some primary results of FNTM are presented for integer- and non-integer-order derivatives in the Riemann–Liouville and Caputo senses under generalized Hukuhara differentiability. The method is illustrated by providing some examples.

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

Ahmadian A, Ismail F, Salahshour S, Baleanu D, Ghaemi F (2017) 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

Alijani Z, Baleanu D, Shiri B, Wu GC (2020) Spline collocation methods for systems of fuzzy fractional differential equations. Chaos Solitons Fractals 131:109510MathSciNetMATH

Alijani Z, Kangro U (2021) On the smoothness of the solution of fuzzy Volterra integral equations of the second kind with weakly singular kernels. Numer Funct Anal Optim 42:819–833MathSciNetMATH

Alijani Z, Kangro U (2022) Numerical solution of a linear fuzzy Volterra integral equation of the second kind with weakly singular kernels. Soft Comput 26:12009–12022

Allahviranloo T, Gouyandeh Z, Armand A, Hasanoglu A (2015) On fuzzy solutions for heat equation based on generalized Hukuhara differentiability. Fuzzy Sets Syst 265:1–23MathSciNetMATH

Allahviranloo T, Ahmadi MB (2010) Fuzzy Laplace transforms. Soft Comput 14:235–243MATH

Allahviranloo T (2021) Fuzzy fractional differential operators and equation, Studies in Fuzziness and Soft Computing, 397

Asiru MA (2002) Further properties of Sumudu Transform and its applications. Int J Math Educ Sci Technol 33(2):441–449MathSciNetMATH

Asiru MA (2003) Classroom note: application of the Sumudu transform to discrete dynamic systems. Int J Math Educ Sci Technol 34:944–949

Baleanu D, Shiri B (2022) Generalized fractional differential equations for past dynamic. AIMS Math 7:14394–14418MathSciNet

Baleanu D, Shiri B (2022) Nonlinear higher order fractional terminal value problems. AIMS Math 7:7489–7506MathSciNet

Bede B, Rudas I, Bencsik A (2007) First order linear fuzzy differential equations under generalized differentiability. Inf Sci 177:1648–1662MathSciNetMATH

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

Belgacem FBM, Karaballi AA, Kalla SL (2003) Analytical investigations of the Sumudu transform and applications to integral production equations. Math Probl Eng 3:103–118MathSciNetMATH

Belgacem FBM (2010) Sumudu transform applications to Bessel’s Functions and Equations. Appl Math Sci 4:3665–3686MathSciNetMATH

da Costa TM, Chalco-Cano Y, Lodwick WA, Silva GN (2018) A new approach to linear interval differential equations as a first step toward solving fuzzy differential. Fuzzy Sets Syst 347:129–141MathSciNetMATH

Debnath L, Bhatta D (2007) Integral transforms and their applications, 2nd edn. C.R.C. Press, LondonMATH

Gasilov NA, Amrahov ŞE, Fatullayev AG (2016) On a solution of the fuzzy Dirichlet problem for the heat equation. Int J Therm Sci 103:67–76

Ghaffari M, Allahviranloo T, Abbasbandy S, Azhini M (2021) On the fuzzy solutions of time-fractional problems. Iranian J Fuzzy Syst 18:51–66MathSciNetMATH

Guo Y, Ye G, Liu W, Zhao D, Treanţă S (2021) Optimality conditions and duality for a class of generalized convex interval-valued optimization problems. Mathematics 9:2979

Guo Y, Ye G, Liu W, Zhao D, Treanţă S (2022) On symmetric gH-derivative: applications to dual interval-valued optimization problems. Chaos Solitons Fractals 158:112068MathSciNetMATH

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, Minh Duc T (2019) Fuzzy fractional differential equations under Caputo Katugampola fractional derivative approach. Fuzzy Sets Syst 375:70–99MathSciNetMATH

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

Khan ZH, Khan WA (2008) N-transform properties and applications. NUST J Eng Sci 1(1):127–133

Keshavarz M, Allahviranloo T (2021) Fuzzy fractional diffusion processes and drug release, Fuzzy Sets and Systems

Kilicman A, Eltayeb, H, Agarwal RP (2010) On Sumudu transform and system of differential equations. Abstr Appl Anal. 2010

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

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

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

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, Pariz N, Kamyad AV (2018) Granular differentiability of fuzzy-number-valued functions. IEEE Trans Fuzzy Syst 26:310–323

Mazandarani M, Zhao Y (2020) Z-differential equations. IEEE Trans Fuzzy Syst 28:462–473

Najariyan M, Zhao Y (2020) On the stability of fuzzy linear dynamical systems. J Franklin Inst 357:5502–5522MathSciNetMATH

Najariyan M, Zhao Y (2017) Fuzzy fractional quadratic regulator problem under granular fuzzy fractional derivatives. IEEE Trans Fuzzy Syst 26:2273–2288

Pedrycz W, Gomide F (1998) An introduction to fuzzy sets: analysis and design, Massachusetts Institute of Technology

Pham VN, Ngo LT, Pedrycz W (2016) Interval-valued fuzzy set approach to fuzzy co-clustering for data classification. Knowl-Based Syst 107:1–13

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

Salahshour S, Allahviranloo T (2013) Applications of fuzzy Laplace transforms. Soft Comput 17:145–158MATH

Schiff LJ (2005) Laplace transform theory and applications, Auckland New-Zealand,. Springer, Berlin

Shiri B (2023) A unified generalization for Hukuhara types differences and derivatives: solid analysis and comparisons. AIMS Math 8:2168–2190MathSciNet

Son NTK, Long HV, Dong NP (2019) Fuzzy delay differential equations under granular differentiability with applications. Comput Appl Math 38:107MathSciNetMATH

Spiegel MR (1965) Theory and problems of Laplace transforms, Schaums outline series. McGraw Hill, New York

Treanţă S (2021) LU-optimality conditions in optimization problems with mechanical work objective functionals. IEEE Trans Neural Netw Learn Syst 33:4971–4978MathSciNet

Treanţă S (2021) On a class of constrained interval-valued optimization problems governed by mechanical work cost functionals. J Optim Theory Appl 188:913–924MathSciNetMATH

Treanţă S (2021) Efficiency in uncertain variational control problems. Neural Comput Appl 33:5719–5732

Treanţă S (2022) Characterization results of solutions in interval-valued optimization problems with mixed constraints. J Global Optim 82:951–964MathSciNetMATH

Treanţă S (2022) Saddle-point optimality criteria involving (p, b, d)-invexity and (p, b, d)-pseudoinvexity in interval-valued optimisation problems. Int J Control 95:1042–1050MathSciNetMATH

Watugala GK (1998) Sumudu transform-a new integral transform to solve differential equations and control engineering problems. Math Eng Ind 6:319–329MathSciNetMATH

Titel: Fuzzy natural transform method for solving fuzzy differential equations
verfasst von: Shabir Ahmad
Aman Ullah
Abd Ullah
Ngo Van Hoa
Publikationsdatum: 14.05.2023
Verlag: Springer Berlin Heidelberg
Erschienen in: Soft Computing / Ausgabe 13/2023
Print ISSN: 1432-7643
Elektronische ISSN: 1433-7479
DOI: https://doi.org/10.1007/s00500-023-08194-w

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