Existence of solutions for a class of nonlinear fractional difference equations of the Riemann–Liouville type View Full Text


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Article Info

DATE

2022-04-18

AUTHORS

Pshtiwan Othman Mohammed, Hari Mohan Srivastava, Juan L. G. Guirao, Y. S. Hamed

ABSTRACT

Nonlinear fractional difference equations are studied deeply and extensively by many scientists by using fixed-point theorems on different types of function spaces. In this study, we combine fixed-point theory with a set of falling fractional functions in a Banach space to prove the existence and uniqueness of solutions of a class of fractional difference equations. The most important part of this article is devoted to correcting a significant mistake made in the literature in using the power rule by providing further conditions for its validity. Also, we provide specific conditions under which difference equations have attractive solutions and the solutions are also asymptotically stable. Furthermore, we construct some fractional difference examples in order to illustrate the validity of the observed results. More... »

PAGES

32

References to SciGraph publications

  • 2019-04-23. Uncertain fractional forward difference equations for Riemann–Liouville type in ADVANCES IN CONTINUOUS AND DISCRETE MODELS
  • 2021-04-29. Analytic and numerical solutions of discrete Bagley–Torvik equation in ADVANCES IN CONTINUOUS AND DISCRETE MODELS
  • 2010-12-20. Existence Results for Nonlinear Fractional Difference Equation in ADVANCES IN CONTINUOUS AND DISCRETE MODELS
  • 2018-04-27. Existence of solutions for fractional difference equations via topological degree methods in ADVANCES IN CONTINUOUS AND DISCRETE MODELS
  • 2015. Discrete Fractional Calculus in NONE
  • 2018-05-22. Positive solutions for a system of first-order discrete fractional boundary value problems with semipositone nonlinearities in REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS, FÍSICAS Y NATURALES. SERIE A. MATEMÁTICAS
  • 2021-04-21. Difference monotonicity analysis on discrete fractional operators with discrete generalized Mittag-Leffler kernels in ADVANCES IN CONTINUOUS AND DISCRETE MODELS
  • 2018-06-15. Monotonicity results for h-discrete fractional operators and application in ADVANCES IN CONTINUOUS AND DISCRETE MODELS
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    URI

    http://scigraph.springernature.com/pub.10.1186/s13662-022-03705-9

    DOI

    http://dx.doi.org/10.1186/s13662-022-03705-9

    DIMENSIONS

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