A new approach to solving local fractional Riccati differential equations using the Adomian-Elzaki method

Hilal Aydemir; Mehmet Merdan; Ümit Demir; Hilal Aydemir; Mehmet Merdan; Ümit Demir

doi:10.3934/math.2025420

AIMS Mathematics

2025, Volume 10, Issue 4: 9122-9149. doi: 10.3934/math.2025420

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A new approach to solving local fractional Riccati differential equations using the Adomian-Elzaki method

1.
Department of Mathematical Engineering, Gumushane University, Gumushane, Turkey
2.
Banking and Insurance Department/Finance, Bayburt University, Bayburt, Turkey

Received: 23 January 2025 Revised: 06 March 2025 Accepted: 20 March 2025 Published: 21 April 2025
MSC : 35C05, 35R11, 65R10

The Elzaki-Adomian decomposition method (EADM) is intended to serve as an efficient analytical method for the resolution of these original fractional-order Riccati differential equations. This can be accomplished permanently by incorporating the Adomian decomposition method with Elzaki. The local fractional derivative is implemented in this format. Particularly in the context of nonlinear differential equations (ODE), this approach is preferred over digital gaps. Additionally, the method's convergence. Random individuals with uniform, beta, normal, and gamma distributions are used to select the initial conditions or coefficients of the equations. The variance, confidence interval, and expected value of the solutions that are obtained will be determined. MATLAB (2013a) package software will be employed to display the individuals that were brought together, and the results will be analyzed randomly.
- local fractional derivative,
- Elzaki-Adomian decomposition method,
- continuous probability distributions,
- expectation value,
- variance
Citation: Hilal Aydemir, Mehmet Merdan, Ümit Demir. A new approach to solving local fractional Riccati differential equations using the Adomian-Elzaki method[J]. AIMS Mathematics, 2025, 10(4): 9122-9149. doi: 10.3934/math.2025420

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Abstract

The Elzaki-Adomian decomposition method (EADM) is intended to serve as an efficient analytical method for the resolution of these original fractional-order Riccati differential equations. This can be accomplished permanently by incorporating the Adomian decomposition method with Elzaki. The local fractional derivative is implemented in this format. Particularly in the context of nonlinear differential equations (ODE), this approach is preferred over digital gaps. Additionally, the method's convergence. Random individuals with uniform, beta, normal, and gamma distributions are used to select the initial conditions or coefficients of the equations. The variance, confidence interval, and expected value of the solutions that are obtained will be determined. MATLAB (2013a) package software will be employed to display the individuals that were brought together, and the results will be analyzed randomly.

References

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