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Vol. 52 No. 1 (2026)
Serdica Mathematical Journal

Articles

Some data dependence results on the solutions of iterative differential equations via a new three-step iteration process

https://doi.org/10.55630/serdica.2026.29-60

Published 13-04-2026

  • Gajanan S. Patil
    • ,
  • Samreen N. Ahmad
    • ,
  • Haribhau L. Tidke

Gajanan S. Patil
PSGVPM's Arts, Science and Commerce College, Shahada

Samreen N. Ahmad
Kavayitri Bahinabai Chaudhari North Maharashtra University

Haribhau L. Tidke
Kavayitri Bahinabai Chaudhari North Maharashtra University

Abstract

In this study, we employ a new three-step iteration method to investigate the existence and uniqueness of the solution to the iterative differential equation of fractional order in the sense of Caputo. We also deal with data dependence results, including dependence on initial data, closeness of solutions, and dependence on the parameters and functions of the solution to the iterative differential equation. Finally, we illustrated all of our conclusions using an example and compared the rate of convergence of a new three-step iteration with other iterative approaches.

2020 Mathematics Subject Classification:

34A12, 26A33, 35B30, 47J25

Keywords

Existence and uniqueness, new iterative method, Fractional derivative, Continuous dependence, closeness, parameters

Full text

Author Details

Gajanan S. Patil

Department of Mathematics
PSGVPM’s ASC College
Shahada, India
e-mail: gajanan.umesh@rediffmail.com

Samreen N. Ahmad

Department of Mathematics
School of Mathematical Sciences
Kavayitri Bahinabai Chaudhari North Maharashtra University
Jalgaon, India
e-mail: samreenahmad11296@gmail.com

Haribhau L. Tidke

Department of Mathematics
School of Mathematical Sciences
Kavayitri Bahinabai Chaudhari North Maharashtra University
Jalgaon, India
e-mail: samreenahmad11296@gmail.com

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