In this paper, we propose the solution of partial Volterra fuzzy integro-differential equation (PVFIDE) with convolution type kernel using two-dimensional fuzzy Sumudu transform (2D-FST) method under Hukuhara differentiability. It is shown that 2D-FST is a simple and reliable approach for solving such equations analytically. Finally, the method is illustrated with example to show the ability of the proposed method.
REFERENCES
1.
Abdul
Rahman
N. A., M. Z.
Ahmad
. Fuzzy Sumudu transform for solving fuzzy partial differential equations
. J. Nonlinear Sci. Appl.
, 9
:3226
–3239
, 2016
.2.
N. A. Abdul
Rahman
, M. Z.
Ahmad
. Solving Fuzzy Volterra Integral Equations via Fuzzy Sumudu Transform
. Appl. Math. Comput. Intell.
, 6
: 19
–28
, 2017
.3.
S.
Abbasbandy
, M.
Hashemi
. A series solution of fuzzy integro-differential equations
. J. Fuzzy Set Valued Anal.
, 00066
, 2012
.4.
J.
Ahmad
, H.
Nosher
. Solution of Different Types of Fuzzy Integro-Differential Equations Via Laplace Homotopy Perturbation Method
, J. Sci. Arts
, 17
, 2017
.5.
A.
Alidema
, A.
Georgieva
. Adomian decomposition method for solving two-dimensional nonlinear Volterra fuzzy integral equations
. AIP Conference Proceedings
, 2048
:050009
, 2018
.6.
A.
Alidema
, A.
Georgieva
. Applications of the double fuzzy Sumudu transform for solving Volterra fuzzy integral equations
. AIP Conference Proceedings
, 2172
:060006
,2019
7.
T.
Allahviranloo
, M.
Kermani
. Numerical methods for fuzzy linear partial differential equations under new definition for derivative
. Iran. J. Fuzzy Syst.
, 7
:33
–50
, 2010
8.
Y.
Chalco-Cano
, H.
Roman-Flores
. On new solutions of fuzzy differential quations
. Chaos Solitons Fractals
, 38
:112
–119
, 2008
.9.
D.
Chalishajar
, R.
Ramesh
. Controllability for impulsive fuzzy neutral functional integro-differential equations
, AIP Conf. Proc
., 12159
, 030007
, 2019
.10.
D.
Dubois
and H.
Prade
. Towards fuzzy differential calculus part 1: Integration of fuzzy mappings
. Journal of Approximation Theory
, 8
:105
–116
, 1982
.11.
M.
Friedman
, M.
Ma
and A.
Kandel
, Numerical solutions of fuzzy differential and integral equations
. Fuzzy Sets Syst.
, 106
:35
–48
, 1999
.12.
A.
Georgieva
. Solving two-dimensional nonlinear Volterra-Fredholm fuzzy integral equations by using Adomian decomposition method
. Dynamic Systems and Applications
, 27
:819
–837
, 2018
.13.
A.
Georgieva
. Double fuzzy Sumudu transform to solve partial Volterra fuzzy integro-differential equations
. Mathematics
, 8
, 692
, 2020
.14.
A.
Georgieva
, A.
Alidema
. Convergence of homotopy perturbation method for solving of two-dimensional fuzzy Volterra functional integral equations
. Advanced Computing in Industrial Mathematics, Studies in Computational Intelligence
, 793
, 2019
.15.
A.
Georgieva
, I.
Naydenova
, Numerical solution of nonlinear Urisohn-Volterra fuzzy functional integral equations
, AIP Conference Proceedings
, 1910
:050010
-1
-050010-8, 2017
.16.
A.
Georgieva
, I.
Naydenova
, Application of homotopy analysis method for solving of two-dimensional linear Volterra fuzzy integral equations
, AIP Conference Proceedings
, 2159
, 030012
, 2019
.17.
A.
Georgieva
, A.
Pavlova
, I.
Naydenova
. Error estimate in the iterative numerical method for two-dimensional nonlinear Hammerstein-Fredholm fuzzy functional integral equations
, Advanced Computing in Industrial Mathematics, Studies in Computational Intelligence
, 728
:41
–45
, 2018
.18.
R.
Goetschel
, W.
Voxman
. Elementary fuzzy calculus
. Fuzzy Sets and Systems.
18
:31
–43
, 1986
.19.
L.
Hooshangian
. Nonlinear Fuzzy Volterra Integro-differential Equation of N-th Order: Analytic Solution and Existence and Uniqueness of Solution
. Int. J. Ind. Math.
, 11
, 12
, 2019
.20.
A.
Kaufmann
, M. M.
Gupta
. Introduction to Fuzzy Arithmetic: Theory and Applications. Van Nostrand Rein-hold Co
.: New York, NY, USA
, 1991
.21.
J.
Mordeson
, W.
Newman
. Fuzzy integral equations
. Inf. Sci.
, 87
:215
–229
, 1995
.22.
S. Min
Kang
, Z.
Iqbal
, M.
Habib
, W.
Nazeer
. Sumudu Decomposition Method for Solving Fuzzy Integro-Differential Equations
. Axioms
, 74
: 2019
.23.
Z.
Majid
, F.
Rabiei
, F.
Hamid
, F.
Ismail
. Fuzzy Volterra Integro-Differential Equations Using General Linear Method
. Symmetry
, 11
:381
–291
, 2019
.24.
I.
Naydenova
, A.
Georgieva
. Approximate solution of nonlinear mixed Volterra-Fredholm fuzzy integral equations using the Adomian method
. AIP Conference Proceedings
, 2172
, 060005
, 2019
.25.
A.
Pavlova
. Quadrature iterative method for a numerical solution of a nonlinear Hammerstein fuzzy functional integral equation
. Journal of the Technical University - Sofia Plovdiv branch, Bulgaria “Fundamental Sciences and Applications”
, 23
:175
–180
, 2017
.26.
A.
Pavlova
, L.
Trenkova
. Existence and uniqueness of two-dimensional nonlinear Urisohn-Volterra fuzzy functional integral equations
. AIP Conference Proceedings
2048
, 050011
, 2018
.27.
M. L.
Puri
, D. A
Ralescu
Differentials of fuzzy functions
. J. Math. Anal. Appl.
, 91
:552
–558
, 1983
.28.
S.
Seikkala
. On the fuzzy initial value problem
. Fuzzy Sets and Systems
, 24
:319
–330
, 1987
.29.
G. K.
Watugala
. The Sumudu transform for functions of two variables
. Math. Eng. Ind.
, 8
:293
–302
, 2002
.30.
H. C.
Wu
. The improper fuzzy Riemann integral and its numerical integration
. Computer Science, Mathematics
, 111
, 1998
.31.
C.
Wu
, Z.
Gong
. On Henstock integral of fuzzy-number-valued functions (1)
. Fuzzy Sets and Systems
, 120
:523
–532
, 2001
.
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