Residual Power Series Method for ψ-Caputo Fractional Differential Equations

Handan Çerdik Yaslan; Anzhelıka Sulemanova

doi:10.54187/jnrs.1862722

Residual Power Series Method for ψ-Caputo Fractional Differential Equations

Abstract

In this paper, linear ψ-Caputo fractional differential equations with constant coefficients and initial conditions are considered. The classic residual power series method is adapted to ψ-Caputo fractional differential equations. An approximate analytical solution of the problem is written as a power series in terms of the function ψ with unknown coefficients. The method can also be applied to the ψ-Caputo fractional relaxation-oscillation equations. Numerical examples substantiate both the scope of applicability and the level of accuracy achieved by the method.

Keywords

The ψ-Caputo fractional derivative, fractional differential equations, residual power series method, relaxationoscillation equations

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Details

Primary Language

English

Subjects

Approximation Theory and Asymptotic Methods

Journal Section

Research Article

Authors

Handan Çerdik Yaslan ^*
0000-0002-3243-3703
Türkiye

Anzhelıka Sulemanova
0009-0005-2025-4213
Türkiye

Publication Date

April 30, 2026

Submission Date

January 13, 2026

Acceptance Date

April 7, 2026

Published in Issue

Year 2026 Volume: 15 Number: 1

DOI

https://doi.org/10.54187/jnrs.1862722

IZ

https://izlik.org/JA78RN38HL

APA

Çerdik Yaslan, H., & Sulemanova, A. (2026). Residual Power Series Method for ψ-Caputo Fractional Differential Equations. Journal of New Results in Science, 15(1), 130-142. https://doi.org/10.54187/jnrs.1862722

AMA

1.Çerdik Yaslan H, Sulemanova A. Residual Power Series Method for ψ-Caputo Fractional Differential Equations. JNRS. 2026;15(1):130-142. doi:10.54187/jnrs.1862722

Chicago

Çerdik Yaslan, Handan, and Anzhelıka Sulemanova. 2026. “Residual Power Series Method for ψ-Caputo Fractional Differential Equations”. Journal of New Results in Science 15 (1): 130-42. https://doi.org/10.54187/jnrs.1862722.

EndNote

Çerdik Yaslan H, Sulemanova A (April 1, 2026) Residual Power Series Method for ψ-Caputo Fractional Differential Equations. Journal of New Results in Science 15 1 130–142.

IEEE

[1]H. Çerdik Yaslan and A. Sulemanova, “Residual Power Series Method for ψ-Caputo Fractional Differential Equations”, JNRS, vol. 15, no. 1, pp. 130–142, Apr. 2026, doi: 10.54187/jnrs.1862722.

ISNAD

Çerdik Yaslan, Handan - Sulemanova, Anzhelıka. “Residual Power Series Method for ψ-Caputo Fractional Differential Equations”. Journal of New Results in Science 15/1 (April 1, 2026): 130-142. https://doi.org/10.54187/jnrs.1862722.

JAMA

1.Çerdik Yaslan H, Sulemanova A. Residual Power Series Method for ψ-Caputo Fractional Differential Equations. JNRS. 2026;15:130–142.

MLA

Çerdik Yaslan, Handan, and Anzhelıka Sulemanova. “Residual Power Series Method for ψ-Caputo Fractional Differential Equations”. Journal of New Results in Science, vol. 15, no. 1, Apr. 2026, pp. 130-42, doi:10.54187/jnrs.1862722.

Vancouver

1.Handan Çerdik Yaslan, Anzhelıka Sulemanova. Residual Power Series Method for ψ-Caputo Fractional Differential Equations. JNRS. 2026 Apr. 1;15(1):130-42. doi:10.54187/jnrs.1862722