jnrs

Journal of New Results in Science

1304-7981

Tokat Gaziosmanpasa University

Approximation Theory and Asymptotic Methods

Yaklaşım Teorisi ve Asimptotik Yöntemler

Residual Power Series Method for ψ-Caputo Fractional Differential Equations

https://orcid.org/0000-0002-3243-3703

Çerdik Yaslan

Handan

PAMUKKALE UNIVERSITY

https://orcid.org/0009-0005-2025-4213

Sulemanova

Anzhelıka

PAMUKKALE ÜNİVERSİTESİ

04 30 2026

15 1 130 142 01 13 2026 04 07 2026

2012

Journal of New Results in Science

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.

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

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