Double Fuzzy Sumudu Transform to Solve Partial Volterra Fuzzy Integro-Differential Equations

“…Bushnaq at al. [9] find solution a fuzzy Volterra Abel's integral equation of the second kind with Laplace -ADM. Georgieva [4,5,14], gave solution two dimensional fuzzy Volterra-Fredholm with Adomain and use double fuzzy Sumudu Transform to solve partial Volterra Fuzzy Integro-Differential Equations and fuzzy Sawi decompositon for nonlinear differential equations. L. Al-Taee at al.…”

Section: Introductionmentioning

confidence: 99%

Applications of Double Fuzzy Sumudu Adomain Decompositon Method for Two-dimensional Volterra Fuzzy Integral Equations

Alidema

2022

Eur. J. Pure Appl. Math.

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In this paper, we combine double Sumudu transform with Adomian decomposition method to solve two dimensional fuzzy convolution Volterra integral equations. We give some definition for fuzzy number, fuzzy valued function which are prerequest for combine the double fuzzy Sumudu transform with Adomian decomposition transform method. We describe the method and finally, numerical examples are given to illustrate the efficiency and applicability of our method.

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“…The IEM performs better than the established approach and is discovered to be in good agreement. Moreover, Georgieva [21] presented the double fuzzy Sumudu transform to solve the partial Volterra fuzzy integro-differential equation with the convolution kernel under H-differentiability. In [22], You, Cheng, and Ma studied the stability of the fuzzy Euler method related to the FDE.…”

Section: Introductionmentioning

confidence: 99%

Incorporating Fuzziness in the Traditional Runge–Kutta Cash–Karp Method and Its Applications to Solve Autonomous and Non-Autonomous Fuzzy Differential Equations

2022

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The study of the fuzzy differential equation is a topic that researchers are interested in these days. By modelling, this fuzzy differential equation can be used to resolve issues in the real world. However, finding an analytical solution to this fuzzy differential equation is challenging. Thus, this study aims to present the fuzziness in the traditional Runge–Kutta Cash–Karp of the fourth-order method to solve the first-order fuzzy differential equation. Later, this method is referred to as the fuzzy Runge–Kutta Cash–Karp of the fourth-order method. There are two types of fuzzy differential equations to be solved: autonomous and non-autonomous fuzzy differential equations. This fuzzy differential equation is divided into the (i) and (ii)–differentiability on the basis of the characterization theorem. The convergence analysis of the fuzzy Runge–Kutta Cash–Karp of the fourth-order method is also presented. By implementing the fuzzy Runge–Kutta Cash–Karp of the fourth-order method, the approximate solution is compared with the analytical and numerical solutions obtained from the fuzzy Runge–Kutta of the fourth-order method. The results demonstrated that the approximate solutions of the proposed method are accurate with an analytical solution, when compared with the solutions of the fuzzy Runge–Kutta of the fourth-order method.

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Double Fuzzy Sumudu Transform to Solve Partial Volterra Fuzzy Integro-Differential Equations

Cited by 23 publications

References 32 publications

Fuzzy Differential Inequalities for Convolution Product of Ruscheweyh Derivative and Multiplier Transformation

Fuzzy Differential Inequalities for Convolution Product of Ruscheweyh Derivative and Multiplier Transformation

Applications of Double Fuzzy Sumudu Adomain Decompositon Method for Two-dimensional Volterra Fuzzy Integral Equations

Incorporating Fuzziness in the Traditional Runge–Kutta Cash–Karp Method and Its Applications to Solve Autonomous and Non-Autonomous Fuzzy Differential Equations

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