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A novel fixed point iteration process applied in solving the Caputo type fractional differential equations in Banach spaces

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  • Godwin Amechi Okeke

    (Functional Analysis and Optimization Research Group Laboratory (FANORG), Department of Mathematics, School of Physical Sciences, Federal University of Technology Owerri, P.M.B. 1526, Owerri, Imo State, Nigeria)

  • Cyril Ifeanyichukwu Ugwuogor

    (Functional Analysis and Optimization Research Group Laboratory (FANORG), Department of Mathematics, School of Physical Sciences, Federal University of Technology Owerri, P.M.B. 1526, Owerri, Imo State, Nigeria)

  • Rubayyi T. Alqahtani

    (��,§Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, Saudi Arabia)

  • Melike Kaplan

    (��Department of Computer Engineering, Faculty of Engineering and Architecture, Kastamonu University, Kastamonu, Türkiye)

  • W. Eltayeb Ahmed

    (��,§Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, Saudi Arabia)

Abstract

We introduce the modified Picard–Ishikawa hybrid iterative scheme and establish some strong convergence results for the class of asymptotically generalized ϕ-pseudocontractive mappings in the intermediate sense in Banach spaces and approximate the fixed point of this class of mappings via the newly introduced iteration scheme. We construct some numerical examples to support our results. Furthermore, we apply the Picard–Ishikawa hybrid iteration scheme in solving the nonlinear Caputo type fractional differential equations. Our results generalize, extend and unify several existing results in literature.

Suggested Citation

  • Godwin Amechi Okeke & Cyril Ifeanyichukwu Ugwuogor & Rubayyi T. Alqahtani & Melike Kaplan & W. Eltayeb Ahmed, 2025. "A novel fixed point iteration process applied in solving the Caputo type fractional differential equations in Banach spaces," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 36(01), pages 1-19, January.
    • Handle: RePEc:wsi:ijmpcx:v:36:y:2025:i:01:n:s0129183124501766
    DOI: 10.1142/S0129183124501766
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