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Impulsive Fractional Differential Equations with Retardation and Anticipation
(2023) Benchohra, Mouffak; Karapınar, Erdal; Lazreg, Jamal Eddine; Salim, Abdelkrim
This chapter deals with the existence and uniqueness results for a class of impulsive initial and boundary value problems for implicit nonlinear fractional differential equations and k-Generalized ψ -Hilfer fractional derivative involving both retarded and advanced arguments. Our results are based on some necessary fixed point theorems. Suitable illustrative examples are provided for each section.
Citation - Scopus: 3
Fractional Gegenbauer Kernel Functions: Theory and Application
(Springer, 2023) Nedaei Janbesaraei, Sherwin; Azmoon, Amirreza; Baleanu, Dumitru
Because of the usage of many functions as a kernel, the support vector machine method has demonstrated remarkable versatility in tackling numerous machine learning issues. Gegenbauer polynomials, like the Chebyshev and Legender polynomials which are introduced in previous chapters, are among the most commonly utilized orthogonal polynomials that have produced outstanding results in the support vector machine method. In this chapter, some essential properties of Gegenbauer and fractional Gegenbauer functions are presented and reviewed, followed by the kernels of these functions, which are introduced and validated. Finally, the performance of these functions in addressing two issues (two example datasets) is evaluated.

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