Fuzzy Solutions of Fuzzy Fractional Parabolic Integro Differential Equations

Nagwa Saeed; Deepak Pachpatte

doi:10.32323/ujma.1631793

EN

Fuzzy Solutions of Fuzzy Fractional Parabolic Integro Differential Equations

Abstract

This work primarily investigates the numerical solution of fuzzy fractional parabolic integro-differential equations of the Volterra type with the time derivative defined in the Caputo sense using the fuzzy Adomian decomposition method. Fuzzy fractional partial integro-differential equations pose significant mathematical challenges due to the interplay between fuzziness and fractional-order dynamics, while at the same time, there is a growing need for accurate and efficient methods to model real-world phenomena involving uncertainty in physics, biology, and engineering. The fuzzy Adomian decomposition method provides an alternative approach for obtaining approximate fuzzy solutions, and its applicability to such equations has not been studied in detail previously in the literature. Furthermore, existence and uniqueness theorems for the fuzzy fractional partial integro-differential equation are established by considering the differentiability type of the solution. The accuracy and efficiency of the proposed method are demonstrated through a series of numerical experiments.

Keywords

Adomian decomposition method, Fixed point theorem, Fuzzy fractional derivative, Fuzzy fractional parabolic equation

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Details

Primary Language

English

Subjects

Numerical Solution of Differential and Integral Equations, Partial Differential Equations

Journal Section

Research Article

Authors

Nagwa Saeed ^*
0000-0002-6731-3971
Yemen

Deepak Pachpatte
0000-0003-3763-4878
India

Early Pub Date

May 29, 2025

Publication Date

June 27, 2025

Submission Date

February 2, 2025

Acceptance Date

May 28, 2025

Published in Issue

Year 2025 Volume: 8 Number: 2

DOI

https://doi.org/10.32323/ujma.1631793

IZ

https://izlik.org/JA64GX84JD

APA

Saeed, N., & Pachpatte, D. (2025). Fuzzy Solutions of Fuzzy Fractional Parabolic Integro Differential Equations. Universal Journal of Mathematics and Applications, 8(2), 81-93. https://doi.org/10.32323/ujma.1631793

AMA

1.Saeed N, Pachpatte D. Fuzzy Solutions of Fuzzy Fractional Parabolic Integro Differential Equations. Univ. J. Math. Appl. 2025;8(2):81-93. doi:10.32323/ujma.1631793

Chicago

Saeed, Nagwa, and Deepak Pachpatte. 2025. “Fuzzy Solutions of Fuzzy Fractional Parabolic Integro Differential Equations”. Universal Journal of Mathematics and Applications 8 (2): 81-93. https://doi.org/10.32323/ujma.1631793.

EndNote

Saeed N, Pachpatte D (June 1, 2025) Fuzzy Solutions of Fuzzy Fractional Parabolic Integro Differential Equations. Universal Journal of Mathematics and Applications 8 2 81–93.

IEEE

[1]N. Saeed and D. Pachpatte, “Fuzzy Solutions of Fuzzy Fractional Parabolic Integro Differential Equations”, Univ. J. Math. Appl., vol. 8, no. 2, pp. 81–93, June 2025, doi: 10.32323/ujma.1631793.

ISNAD

Saeed, Nagwa - Pachpatte, Deepak. “Fuzzy Solutions of Fuzzy Fractional Parabolic Integro Differential Equations”. Universal Journal of Mathematics and Applications 8/2 (June 1, 2025): 81-93. https://doi.org/10.32323/ujma.1631793.

JAMA

1.Saeed N, Pachpatte D. Fuzzy Solutions of Fuzzy Fractional Parabolic Integro Differential Equations. Univ. J. Math. Appl. 2025;8:81–93.

MLA

Saeed, Nagwa, and Deepak Pachpatte. “Fuzzy Solutions of Fuzzy Fractional Parabolic Integro Differential Equations”. Universal Journal of Mathematics and Applications, vol. 8, no. 2, June 2025, pp. 81-93, doi:10.32323/ujma.1631793.

Vancouver

1.Nagwa Saeed, Deepak Pachpatte. Fuzzy Solutions of Fuzzy Fractional Parabolic Integro Differential Equations. Univ. J. Math. Appl. 2025 Jun. 1;8(2):81-93. doi:10.32323/ujma.1631793