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    A cotangent fractional Gronwall inequality with applications
    (Amer Inst Mathematical Sciences-Aims, 2024) Sadek, Lakhlifa; Akgul, Ali; Bataineh, Ahmad Sami; Hashim, Ishak
    This article presents the cotangent fractional Gronwall inequality, a novel understanding of the Gronwall inequality within the context of the cotangent fractional derivative. We furnish an explanation of the cotangent fractional derivative and emphasize a selection of its distinct characteristics before delving into the primary findings. We present the cotangent fractional Gronwall inequality (Lemma 3.1) and a Corollary 3.2 using the Mittag-Leffler function, we establish singularity and compute an upper limit employing the Mittag-Leffler function for solutions in a nonlinear delayed cotangent fractional system, illustrating its practical utility. To underscore the real -world relevance of the theory, a tangible instance is given.
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    Öğe
    New Properties for Conformable Fractional Derivative and Applications
    (Natural Sciences Publishing, 2024) Sadek, Lakhlifa; Akgül, Ali
    The fractional derivative (FD) has recently captured the minds of scientists. The most common are Riemann-Liouville (RL) and Caputo (C). These fractional derivatives have been used to successfully model many real-world problems due to their physical properties. In 2014, Khalil et al introduced a new definition of an FD called the conformable FD (CFD). In this work, we introduce new properties and theorems related to this new derivative, such as the CFD of the reciprocal function, power of function, exponential of function, and the ?-Leibniz integral rule used to solve fractional differential equations as in the applications section. © 2024 NSP Natural Sciences Publishing Cor.