Nonlinear Fuzzy Volterra Integro-di erential Equation of N-th Order: Analytic Solution and Existence and Uniqueness of Solution

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Hooshangian L.

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Journal: International Journal of Industrial Mathematics Year:2019 | Volume:11 | Issue:1 Page(s): 43-54

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Title

Nonlinear Fuzzy Volterra Integro-di erential Equation of N-th Order: Analytic Solution and Existence and Uniqueness of Solution

Author(s)

Hooshangian L. | Issue Writer Certificate

Keywords

General n􀀀

th order derivative

H-derivative

Fuzzy n􀀀

th Order Integro-di

erential Equation

Existence and Uniqueness theorem

Upper boundary of solution

Abstract

Integro-di erential Equations play a fundamental role in various elds of applied mathematics. The solutions of many engineering problems in general and mechanics and physics in particular, lead to this kind of equations. This paper focuses on the fuzzy Volterra integro-di erential Equation of n􀀀 th order of the second-kind with nonlinear fuzzy kernel and initial values. This equation is transformed to a nonlinear fuzzy Volterra integral equation in multi-integrals by application of a certain analytic solution adapted on Fuzzy n􀀀; th order derivation under generalized Hakuhara derivative. The derived integral equations are solvable, the solutions of which are unique under certain conditions. The existence and uniqueness of the solutions are investigated in a theorem and an upper boundary is found for solutions. An easily-followed algorithm is provided to illustrate the process. The application of the proposed method helps solving the equation on the basis of the Adomian decomposition method under generalized H-derivation. Comparison of the exact and approximated solutions shows the least error.

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APA: Copy

Hooshangian, L.. (2019). Nonlinear Fuzzy Volterra Integro-di erential Equation of N-th Order: Analytic Solution and Existence and Uniqueness of Solution. INTERNATIONAL JOURNAL OF INDUSTRIAL MATHEMATICS, 11(1), 43-54. SID. https://sid.ir/paper/739259/en

Vancouver: Copy

Hooshangian L.. Nonlinear Fuzzy Volterra Integro-di erential Equation of N-th Order: Analytic Solution and Existence and Uniqueness of Solution. INTERNATIONAL JOURNAL OF INDUSTRIAL MATHEMATICS[Internet]. 2019;11(1):43-54. Available from: https://sid.ir/paper/739259/en

IEEE: Copy

L. Hooshangian, “Nonlinear Fuzzy Volterra Integro-di erential Equation of N-th Order: Analytic Solution and Existence and Uniqueness of Solution,” INTERNATIONAL JOURNAL OF INDUSTRIAL MATHEMATICS, vol. 11, no. 1, pp. 43–54, 2019, [Online]. Available: https://sid.ir/paper/739259/en

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