Existence and Uniqueness Solutions of Fuzzy Fractional Integral Equation of Volterra-Stieltjes Type
Анотація
In this paper, we establish the existence and uniqueness results to the Cauchy problem posed for a fuzzy fractional Volterra-Stieltjes integrodifferential equation. The method of successive approximations is used to prove the existence, whereas the contraction theory is applied to prove the uniqueness of the solution to the problem.
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R. P. Agarwal, D. Baleanu, J.J. Nieto, D. F. Torres, Y. Zhou, A survey on fuzzy fractional differential and optimal control nonlocal evolution equations, Journal of Computational and Applied Mathematics, 339, (2018), 3-29.
A.A. Alderremy, J.F. Gomez-Aguilar, A. Shaban, M. S. Khaled, A fuzzy fractional model of coronavirus (COVID-19) and its study with Legendre spectral method, Results in Physics, 21, (2021), 103773.
R. Alikhani, F. Bahrami, Global solutions for nonlinear fuzzy fractional integral and integrodifferential equations, Communications in Nonlinear Science and Numerical Simulation, 18, (2013), 2007-2017.
T. Allahviranloo, S. Abbasbandy, S. Salahshour, Fuzzy fractional differential equations with Nagumo and Krasnoselskii-Krein condition, In Proceedings of the 7th conference of the European Society for Fuzzy Logic and Technology, (2011), 1038-1044, Atlantis Press.
T. Allahviranloo, A. Armand, Z. Gouyandeh, H. Ghadiri1, Existence and uniqueness of solutions for fuzzy fractional Volterra-Fredholm integro-differential equations, Journal of Fuzzy Set Valued Analysis, (2013), 1-9.
J. Banas, Some properties of Urysohn-Stieltjes integral operators, International Journal of Mathematics and Mathematical Sciences, 21, (1), (1998), 79-88.
J. Banas, J.Dronka, Integral operators of Volterra-Stieltjes type, their properties and applications, Mathematical and computer modelling, 32, (11-13), (2000), 1321-1331.
J. Banas, J. R. Rodriguez, K. Sadarangani, On a class of Urysohn-Stieltjes quadratic integral equations and their applications, Journal of computational and applied mathematics, 113, (1), (2000), 35-50.
J. Banas, K.Sadarangani, Solvability of Volterra-Stieltjes operator-integral equations and their applications, Computers & Mathematics with Applications, 41, (12), (2001), 1535-1544.
Z. Deng, Fuzzy pseudo-metric spaces, Journal of Mathematical Analysis and Applications, 86, (1), (1982), 74-95.
A. Dwivedi, G. Rani, G.R. Gautam, Existence of solutions of fuzzy fractional differential equations, Palestine Journal of Mathematics, 11, (2022), 125-132.
A. George, P. Veeramani, On some results in fuzzy metric spaces, Fuzzy sets and systems, 64, (3), (1994), 395-399.
V. Gregori, S. Morillas, A. Sapena, Examples of fuzzy metrics and applications Systems, Fuzzy sets and systems, 170, (1), (2011), 95-111.
F.Y. Ishak, Existence Solution for Nonlinear System of Fractional Integrodifferential Equations of Volterra Type with Fractional Boundary Conditions, Jurnal Matematika MANTIK, 6, (1), (2020), 1-12.
F.Y. Ishak, Existence, uniqueness and stability solution for new system of integrodifferential equation of Volterra type, E-Jurnal Matematika, 9, (2), (2020), 109-116.
O. Kaleva, Fuzzy differential equations, Fuzzy sets and systems, 24, (3), (1987), 301-317.
H.Kestelman, Modern Theories of Integration, Dover, 2nd Edition, (1960), 247-269.
I. Kramosil, J. Michalek, Fuzzy metrics and statistical metric spaces, Kybernetika, 11, (5), (1975), 336-344.
V. Lupulescu, On a class of fuzzy functional differential equations, Fuzzy Sets and Systems, 160, (11), (2009), 1547-1562.
M. Nagarajan, B. Radhakrishnan, P. Anukokila, Existencs results for Sobolev type fuzzy integrodifferntial evolution equation, Palestine Journal of Mathematics, 11, (2022).
C.V. Negoita, D.A. Ralescu , Applications of fuzzy sets to systems analysis, p. 187, Basel, Switzerland, Birkhauser.
J.Y. Park, H.K. Han, Existence and uniqueness theorem for a solution of fuzzy differential equations, Journal of Mathematics and Mathematical Sciences, 22, (2), (1999), 271-279.
A.V. Plotnikov, N.V. Skripnik, New definition of a generalized fuzzy derivative, Journal of Advanced Research in Pure Mathematics, 6, (3), (2014), 69-77.
M.L. Puri, D.A. Ralescu, L. Zadeh, Fuzzy random variables, Readings in fuzzy sets for intelligent systems, (1993), 265-271, Morgan Kaufmann.
L.A. Zadeh, A note on prototype theory and fuzzy sets, Fuzzy Sets, Fuzzy Logic, And Fuzzy Systems, Selected Papers by Lotfi A. Zadeh, (1996), 587-593.
DOI: http://dx.doi.org/10.15421/142210
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