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Browsing by Author "Vivas-Cortez, Miguel"

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    A New Formulation and Analytical Applications of Fractional Operators
    (World Scientific Publ Co Pte Ltd, 2024) Mehmood, Ahsan; Samraiz, Muhammad; Liu, Zhi-Guo; Baleanu, Dumitru; Vivas-Cortez, Miguel; Matematik
    This research paper introduces a novel formulation of the modified Atangana-Baleanu (AB) Fractional Operators (FrOs). The paper begins by discussing the boundedness of the novel fractional derivative operator. Some fractional differential equations corresponding to different choices of functions as well as comparative graphical representations of a function and its derivative are provided. Furthermore, the paper investigates the generalized Laplace transform for this newly introduced operator. By employing the generalized Laplace transform, a wide range of fractional differential equations can be effectively solved. Additionally, the paper establishes the corresponding form of the AB Caputo fractional integral operator, examines its boundedness and obtains its Laplace transform. It is worth noting that the FrOs previously documented in the existing literature can be derived as special cases of these recently explored FrOs.
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    Citation - WoS: 25
    Citation - Scopus: 25
    Some modifications in conformable fractional integral inequalities
    (Springer, 2020) Baleanu, Dumitru; Mohammed, Pshtiwan Othman; Vivas-Cortez, Miguel; Rangel-Oliveros, Yenny; 56389; Matematik
    The prevalence of the use of integral inequalities has dramatically influenced the evolution of mathematical analysis. The use of these useful tools leads to faster advances in the presentation of fractional calculus. This article investigates the Hermite-Hadamard integral inequalities via the notion of F-convexity. After that, we introduce the notion of F-mu-convexity in the context of conformable operators. In view of this, we establish some Hermite-Hadamard integral inequalities (both trapezoidal and midpoint types) and some special case of those inequalities as well. Finally, we present some examples on special means of real numbers. Furthermore, we offer three plot illustrations to clarify the results.