The need to accurately model nonlocal phenomena has motivated the development of various fractional derivative operators
Research gap analysis derived from 3 mathematics papers in our local library.
The gap
The need to accurately model nonlocal phenomena has motivated the development of various fractional derivative operators. A gap in the literature on nonlinear Cauchy problems driven by hybrid proportional-Caputo fractional derivatives in Banach spaces is identified.
Evidence profile
Sourced from the stated challenges and stated research gap of the source papers, classified as general, spanning 3 journals.
Research trend
Established — well-defined area with open sub-problems.
Supporting evidence — 3 representative gaps
- 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 5/5Keywords: complexity fractional calculus caputo derivative need unified analytical - Cauchy Problem Involving Hybrid Proportional–Caputo Derivative in Banach Spaces (2026) · Contemporary Mathematics · doi
The need to accurately model nonlocal phenomena has motivated the development of various fractional derivative operators. A gap in the literature on nonlinear Cauchy problems driven by hybrid proportional-Caputo fractional derivatives in Banach spaces is identified.
generalstated research gapevidence 5/5Keywords: need accurately model nonlocal phenomena has motivated development - Existence and Uniqueness Results for Tripled Systems Involving Sequential Caputo Fractional Derivatives (2026) · International Journal of Analysis and Applications · doi
The complexity of the tripled system involving sequential Caputo fractional derivatives. The need to establish existence and uniqueness results for the considered system. The challenge of demonstrating the efficiency of fractional techniques in extending classical analytical methods.
generalstated challengesevidence 5/5Keywords: complexity tripled system involving sequential caputo fractional derivatives
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