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Some properties of a class of holomorphic functions associated with tangent function

Khan Muhammad Ghaffar, Mashwani Wali Khan, Salleh Zabidin, Tchier Fairouz, Khan Bilal, Malik Sarfraz Nawaz

Demonstratio Mathematica

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2024

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Vol. 57, nr 1

art. no. 20230142

EN

In this study, we define new class of holomorphic functions associated with tangent function. Furthermore, we examine the differential subordination implementation results related to Janowski and tangent functions. Also, we investigate some extreme point theorem and partial sums results, necessary and sufficient conditions, convex combination, closure theorem, growth and distortion bounds, and radii of close-to-starlikeness and starlikeness for this newly defined functions class of holomorphic functions.

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LADM procedure to find the analytical solutions of the nonlinear fractional dynamics of partial integro-differential equations

Khan Qasim, Khan Hassan, Kumam Poom, Tchier Fairouz, Singh Gurpreet

Demonstratio Mathematica

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2024

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Vol. 57, nr 1

art. no. 20230101

EN

Generally, fractional partial integro-differential equations (FPIDEs) play a vital role in modelling various complex phenomena. Because of the several applications of FPIDEs in applied sciences, mathematicians have taken a keen interest in developing and utilizing the various techniques for its solutions. In this context, the exact and analytical solutions are not very easy to investigate the solution of FPIDEs. In this article, a novel analytical approach that is known as the Laplace adomian decomposition method is implemented to calculate the solutions of FPIDEs. We obtain the approximate solution of the nonlinear FPIDEs. The results are discussed using graphs and tables. The graphs and tables have shown the greater accuracy of the suggested method compared to the extended cubic-B splice method. The accuracy of the suggested method is higher at all fractional orders of the derivatives. A sufficient degree of accuracy is achieved with fewer calculations with a simple procedure. The presented method requires no parametrization or discretization and, therefore, can be extended for the solutions of other nonlinear FPIDEs and their systems.

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Rejection and symmetric difference of bipolar picture fuzzy graph

Almousa Maha Mohammed, Tchier Fairouz

Demonstratio Mathematica

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2023

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Vol. 56, nr 1

art. no. 20230107

EN

Due to the absence of a negative of three membership functions, there are drawbacks to the existing definition of a picture fuzzy graph (PFG). In that definition of bipolar picture fuzzy graph (BPFG), membership function, neutral membership function, nonmembership function, negative of membership function, negative of neutral membership function, and negative of nonmembership function are involved. A BPFG is the extension of PFG. In this manuscript, we present some properties of symmetric difference, and rejection of BPFG.