The application of the proposed method to other complex

The gap

Evidence profile

Sourced from the stated research gap and future-work section and stated challenges and conclusions of the source papers, classified as general, spanning 5 journals.

Supporting evidence — 8 representative gaps

• Adams-Bashforth Scheme and Kayo-Kengne-Akgül Derivative: Connexion and Chaotic Modelling (2026) · Universal Journal of Mathematics and Applications · doi

  The lack of a numerical scheme for solving fractional differential equations involving the Kayo-Kengne-Akgül derivative. The need for a method that can accurately model complex phenomena.

  generalstated research gap
  Keywords: lack numerical scheme solving fractional differential equations involving
• A Haar wavelet operational matrix method for fractional Riccati differential equations with Atangana’s beta derivative (2026) · Advances in Differential Equations and Control Processes · doi

  There is a need for reliable and efficient numerical methods for solving fractional differential equations. The proposed method fills this gap by providing a simple and efficient framework for solving fractional Riccati differential equations.

  generalstated research gapevidence 5/5
  Keywords: there need reliable efficient numerical methods solving fractional
• A Haar wavelet operational matrix method for fractional Riccati differential equations with Atangana’s beta derivative (2026) · Advances in Differential Equations and Control Processes · doi

  To apply the proposed method to other types of fractional differential equations. To compare the proposed method with other numerical methods. To use the proposed method to solve real-world problems involving fractional calculus.

  generalfuture-work sectionevidence 5/5
  Keywords: apply proposed method other types fractional differential equations
• Generalized Laplace Transform Approach to Modelling a Caputo Fractional Differential Equation Involving the Appell Function $F_3$ (2026) · Journal of Mathematical Sciences and Modelling · doi

  The lack of a unified analytical setting for fractional modelling of multivariable special functions and fractional differential equations. The need for a new concept of fractional modelling that can effectively represent systems governed by fractional dynamics and multivariable functional structures.

  generalstated research gapevidence 5/5
  Keywords: lack unified analytical setting fractional modelling multivariable special
• Generalized Laplace Transform Approach to Modelling a Caputo Fractional Differential Equation Involving the Appell Function $F_3$ (2026) · Journal of Mathematical Sciences and Modelling · doi

  To further develop the proposed modelling framework for other types of fractional differential equations. To apply the proposed modelling framework to various disciplines, including physics, engineering, biology, and control theory. To investigate the numerical implementation of the proposed modelling framework.

  generalfuture-work sectionevidence 5/5
  Keywords: further develop proposed modelling framework other types fractional
• Generalized Laplace Transform Approach to Modelling a Caputo Fractional Differential Equation Involving the Appell Function $F_3$ (2026) · Journal of Mathematical Sciences and Modelling · doi

  The complexity of fractional calculus and the Caputo derivative. The need for a unified analytical setting for fractional modelling of multivariable special functions and fractional differential equations. The challenge of deriving a transform representation for the Appell function F 3.

  generalstated challengesevidence 5/5
  Keywords: complexity fractional calculus caputo derivative need unified analytical
• Integrated Mahgoub–VIM Hybrid Transform Technique for Solving Linear, Nonlinear, and Fractional Differential Equations (2026) · Asian Journal of Science Technology Engineering and Art · doi

  Conventional integral transform techniques are inadequate for solving nonlinear and fractional-order differential equations. A comprehensive framework for assessing and comparing hybrid methods is lacking.

  generalstated research gapevidence 5/5
  Keywords: conventional integral transform techniques inadequate solving nonlinear fractional-order
• EQUIVALENCE OF INITIAL CONDITIONS FOR A FRACTIONAL DIFFERENTIAL EQUATION WITH THE RIEMANN–LIOUVILLE DERIVATIVE (2026) · Zenodo (CERN European Organization for Nuclear Research) · doi

  These findings can be used in further studies of fractional models and in trans- forming problems into more applicable forms, such as the Caputo formulation.

  generalconclusionsevidence 4/5
  Keywords: used further fractional models trans forming problems applicable forms caputo formulation

Questions about this gap