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http://dx.doi.org/10.14403/jcms.2022.35.2.177

THE DOUBLE FUZZY ELZAKI TRANSFORM FOR SOLVING FUZZY PARTIAL DIFFERENTIAL EQUATIONS  

Kshirsagar, Kishor A. (Department of Mathematics New Arts, Commerce and Science Autonomous College)
Nikam, Vasant R. (Department of Mathematics Mahatma Gandhi Vidyamandir's, Samajshree Prashantdada Hiray Arts, Science and Commerce College)
Gaikwad, Shrikisan B. (Department of Mathematics New Arts, Commerce and Science Autonomous College)
Tarate, Shivaji A. (Department of Mathematics New Arts, Commerce and Science Autonomous College)
Publication Information
Journal of the Chungcheong Mathematical Society / v.35, no.2, 2022 , pp. 177-196 More about this Journal
Abstract
The Elzaki Transform method is fuzzified to fuzzy Elzaki Transform by Rehab Ali Khudair. In this article, we propose a Double fuzzy Elzaki transform (DFET) method to solving fuzzy partial differential equations (FPDEs) and we prove some properties and theorems of DFET, fundamental results of DFET for fuzzy partial derivatives of the nth order, construct the Procedure to find the solution of FPDEs by DFET, provide duality relation of Double Fuzzy Laplace Transform (DFLT) and Double Fuzzy Sumudu Transform(DFST) with proposed Transform. Also we solve the Fuzzy Poisson's equation and fuzzy Telegraph equation to show the DFET method is a powerful mathematical tool for solving FPDEs analytically.
Keywords
Fuzzy Laplace Transform; Double fuzzy Elzaki Transform; Fuzzy partial differential equations;
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1 T. M. Elzaki, The new integral transform "Elzaki transform", Glob. J. Pure Appl. Math., 7 (2011), no. 1, 57-64.
2 R. G. Moghaddam and T. Allahviranloo, On the fuzzy Poisson equation, Fuzzy Sets Syst., 347 (2018), 105-128.   DOI
3 T. Allahviranloo, Fuzzy fractional differential equations, Stud. Fuzziness Soft Comput., 397 (2021), 127-192.   DOI
4 H. C. Wu, The fuzzy Riemann integral and its numerical integration, Fuzzy Sets Syst., 110 (2000), no. 1, 1-25.   DOI
5 Y. Chalco-Cano and H. Roman-Flores, On new solutions of fuzzy differential equations, Chaos Solit. Fractals, 38 (2008), no. 1, 112-119.   DOI
6 S. Salahshour and T. Allahviranloo, Applications of fuzzy Laplace transforms, Soft Comput., 17 (2013), no. 1, 145-158.   DOI
7 J. J. Buckley and T. Feuring, Introduction to fuzzy partial differential equations, Fuzzy Sets Syst., 105 (1999), no. 2, 241-248.   DOI
8 B. Bede, I. J. Rudas, and A. L. Bencsik, First order linear fuzzy differential equations under generalized differentiability, Inf. Sci., 177 (2007), no. 7, 1648- 1662.   DOI
9 C. J. Tranter, The use of the mellin transform in finding the stress distribution in an infinite wedge, Q. J. Mech. Appl. Math., 1 (1948), no. 1, 125-130.   DOI
10 D. Dubois and H. Prade, Fundamentals of Fuzzy Sets the Handbooks, The Handbooks of Fuzzy Sets Series. Boston, MA: Springer US, 7 (2000).
11 M. Friedman, M. Ma, and A. Kandel, Numerical solutions of fuzzy differential and integral equations, Fuzzy Sets Syst., 106 (1999), no. 1, 35-48.   DOI
12 M. Z. Ahmad and B. De Baets, A predator-prey model with fuzzy initial populations, 2009 International Fuzzy Systems Association World Congress and 2009 European Society for Fuzzy Logic and Technology Conference, IFSA-EUSFLAT 2009 - Proceedings, (2009), 1311-314.
13 T. Allahviranloo, N. A. Kiani, and N. Motamedi, Solving fuzzy differential equations by differential transformation method, Inf. Sci., 179 (2009), no. 7, 956-966.   DOI
14 H. C. Wu, The improper fuzzy Riemann integral and its numerical integration, Inf. Sci., 111 (1998), no. 1-4, 109-137.   DOI
15 A. Khastan, F. Bahrami, and K. Ivaz, New results on multiple solutions for Nthorder fuzzy differential equations under generalized differentiability, Bound. Value Probl., 2009 (2009), 1-13.
16 T. Allahviranloo and M. A. Kermani, Numerical methods for fuzzy linear partial differential equations under new definition for derivative, IJFS., 7 (2010), no. 3, 33-50.
17 T. Allahviranloo and M. B. Ahmadi, Fuzzy Laplace transforms, Soft Comput., 14 (2010), no. 3, 235-243.   DOI
18 A. Georgieva, Double fuzzy sumudu transform to solve partial volterra fuzzy integro-differential equations, Mathematics, 8 (2020), no. 5, 692.   DOI
19 M. S. Hashemi and J. Malekinagad, Series solution of fuzzy wave-like equations with variable coefficients, J. Intell. Fuzzy Syst., 25 (2013), no. 2, 415-428.   DOI
20 S. S. Chang and L. A. Zadeh, On Fuzzy Mapping and Control, IEEE Trans. Syst. Man Cybern. Syst. IEEE T SYST MAN CY-S., SMC-2 (1972), no. 1, 30-34.
21 N. A. A. Rahman and M. Z. Ahmad, Solution of fuzzy partial differential equations using fuzzy Sumudu transform, AIP Conf Proc., 1775 (2016), no. 1, 030018.   DOI
22 J. W. Layman, The Hankel transform and some of its properties, J. Integer Seq., 4 (2001), no. 1, 1-11.
23 A. Georgieva, Application of double fuzzy natural transform for solving fuzzy partial equations, AIP Conf Proc., 2333 (2021), no. 1, 080006.   DOI
24 S. Seikkala, On the fuzzy initial value problem, Fuzzy Sets Syst., 24 (1987), no. 3, 319-330.   DOI
25 R. A. Khudair, A. N. Alkiffai, and A. N. Albukhuttar, Solving the Vibrating Spring Equation Using Fuzzy Elzaki Transform, Math. Model. Eng. Probl., 7 (2020), 549-555.   DOI
26 R. M. Shabestari and R. Ezzati, The Fuzzy Double Laplace Transforms and their Properties with Applications to Fuzzy Wave Equation, New Math. Nat. Comput., 17 (2021), no. 2, 319-338.   DOI
27 S. Chakraverty, S. Tapaswini, and D. Behera, Fuzzy Fractional Telegraph Equations, Fuzzy Arbitrary Order System, 64 (2016), no. 2, 191-206.