10.1007/s40096-022-00458-0

Solvability of some fractional differential equations in the Hölder space Hγ(R+) and their numerical treatment via measures of noncompactness

  • Hojjatollah Amiri Kayvanloo1,
  • Mohammad Mursaleen*2,
  • Mohammad Mehrabinezhad1,
  • Farzaneh Pouladi Najafabadi1,
  1. Department of Mathematics, Islamic Azad University, Mashhad, IR
  2. Department of Medical Research, China Medical University Hospital, China Medical University (Taiwan), Taichung, TW Aligarh Muslim University, Aligarh, 202002, IN

Published in Issue 2022-03-02

Copyright (c) -1 Copyright © 2024, The Author(s), under exclusive licence to Islamic Azad University

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This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Amiri Kayvanloo, H., Mursaleen, M., Mehrabinezhad, M., & Pouladi Najafabadi, F. (2022). Solvability of some fractional differential equations in the Hölder space Hγ(R+) and their numerical treatment via measures of noncompactness. Mathematical Sciences, 17(4 (December 2023). https://doi.org/10.1007/s40096-022-00458-0
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Abstract

Abstract We study the following fractional boundary value problem: Dαυ(t)+f(t,υ(t))=0,α∈(1,2],0

 

The goal of this paper is to bring forward a new family of measures of noncompactness and prove a fixed point theorem of Darbo type in the Hölder space . Moreover, we provide an example which supports our main result and in carrying out an proximate solution for the mentioned example with high precision we apply several numerical methods.

Keywords

  • Darbo’s theorem,
  • Measures of noncompactness,
  • Fractional differential equations,
  • Homotopy perturbation method,
  • Integral equation

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