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δ-β-Gabor integral operators for a space of locally integrable generalized functions
(Springer, 2020) Al-Omari, Shrideh Khalaf; Baleanu, Dumitru; Nisar, Kottakkaran Sooppy
In this article, we give a definition and discuss several properties of the δ-β-Gabor integral operator in a class of locally integrable Boehmians. We derive delta sequences, convolution products and establish a convolution theorem for the given δ-β-integral. By treating the delta sequences, we derive the necessary axioms to elevate the δ-β-Gabor integrable spaces of Boehmians. The said generalized δ-β-Gabor integral is, therefore, considered as a one-to-one and onto mapping continuous with respect to the usual convergence of the demonstrated spaces. In addition to certain obtained inversion formula, some consistency results are also given.
Analysis of the model of HIV-1 infection of CD4(+) T-cell with a new approach of fractional derivative
(Springer, 2020) Baleanu, Dumitru; Mohammadi, Hakimeh; Rezapour, Shahram
By using the fractional Caputo-Fabrizio derivative, we investigate a new version for the mathematical model of HIV. In this way, we review the existence and uniqueness of the solution for the model by using fixed point theory. We solve the equation by a combination of the Laplace transform and homotopy analysis method. Finally, we provide some numerical analytics and comparisons of the results.

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