A Predictor–Corrector Method for Conformable Fractional Differential Equations of Order α ∈ (1,2]

Şuayip Toprakseven

A Predictor–Corrector Method for Conformable Fractional Differential Equations of Order α ∈ (1,2]

Abstract

In this paper, we develop a predictor–corrector numerical method for solving conformable fractional differential equations of order α ∈ (1,2. By transforming the conformable fractional problem into an equivalent system of first-order ordinary differential equations, we construct an Adams–Bashforth–Moulton type scheme adapted to the conformable framework. The proposed method is easy to implement and avoids memory effects typical of Caputo-type fractional models. A consistency and convergence analysis is provided, and the method achieves second-order accuracy under suitable smoothness assumptions

Keywords

References

I. Podlubny, Fractional Differential Equations. San Diego, CA, USA: AcademicPress, 1999.
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M. Yavuz and B. Yaşkıran, "Approximate-analytical solutions of cable equation usingconformable fractional operator," New Trends in Mathematical Sciences, vol. 5, no.4, pp. 209–219, 2017. doi: 10.20852/ntmsci.2017.232.
Ş. Toprakseven, "Numerical solutions of conformable fractional differential equa-tions by Taylor and finite difference methods," Süleyman Demirel Üniver-sitesi Fen Bilimleri Enstitüsü Dergisi, vol. 23, no. 3, pp. 850–863, 2019. doi:10.19113/sdufenbed.579361.94

Details

Primary Language

English

Subjects

Numerical Solution of Differential and Integral Equations

Journal Section

Research Article

Authors

Şuayip Toprakseven ^* This is me
0000-0003-3901-9641
Türkiye

Publication Date

June 30, 2026

Submission Date

May 17, 2026

Acceptance Date

June 11, 2026

Published in Issue

Year 2026 Volume: 3 Number: 3(1)

IZ

https://izlik.org/JA75EG27XR

Cite

RIS / Bibtex

APA

Toprakseven, Ş. (2026). A Predictor–Corrector Method for Conformable Fractional Differential Equations of Order α ∈ (1,2]. Türkiye Mathematical Sciences, 3(3(1), 86-94. https://izlik.org/JA75EG27XR

AMA

1.Toprakseven Ş. A Predictor–Corrector Method for Conformable Fractional Differential Equations of Order α ∈ (1,2]. TMS. 2026;3(3(1):86-94. https://izlik.org/JA75EG27XR

Chicago

Toprakseven, Şuayip. 2026. “A Predictor–Corrector Method for Conformable Fractional Differential Equations of Order α ∈ (1,2]”. Türkiye Mathematical Sciences 3 (3(1): 86-94. https://izlik.org/JA75EG27XR.

EndNote

Toprakseven Ş (June 1, 2026) A Predictor–Corrector Method for Conformable Fractional Differential Equations of Order α ∈ (1,2]. Türkiye Mathematical Sciences 3 3(1) 86–94.

IEEE

[1]Ş. Toprakseven, “A Predictor–Corrector Method for Conformable Fractional Differential Equations of Order α ∈ (1,2]”, TMS, vol. 3, no. 3(1), pp. 86–94, June 2026, [Online]. Available: https://izlik.org/JA75EG27XR

ISNAD

Toprakseven, Şuayip. “A Predictor–Corrector Method for Conformable Fractional Differential Equations of Order α ∈ (1,2]”. Türkiye Mathematical Sciences 3/3(1) (June 1, 2026): 86-94. https://izlik.org/JA75EG27XR.

JAMA

1.Toprakseven Ş. A Predictor–Corrector Method for Conformable Fractional Differential Equations of Order α ∈ (1,2]. TMS. 2026;3:86–94.

MLA

Toprakseven, Şuayip. “A Predictor–Corrector Method for Conformable Fractional Differential Equations of Order α ∈ (1,2]”. Türkiye Mathematical Sciences, vol. 3, no. 3(1), June 2026, pp. 86-94, https://izlik.org/JA75EG27XR.

Vancouver

1.Şuayip Toprakseven. A Predictor–Corrector Method for Conformable Fractional Differential Equations of Order α ∈ (1,2]. TMS [Internet]. 2026 Jun. 1;3(3(1):86-94. Available from: https://izlik.org/JA75EG27XR