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Involvement of three successive fractional derivatives in a system of pantograph equations and studying the existence solution and MLU stability

Hammad Hasanen A., Işık Hüseyin, Aydi Hassen, De la Sen Manuel

Demonstratio Mathematica

2024

Vol. 57, nr 1

art. no. 20240035

Developing a model of fractional differential systems and studying the existence and stability of a solution is considebly one of the most important topics in the field of analysis. Therefore, this manuscript was dedicated to deriving a new type of fractional system that arises from the combination of three sequential fractional derivatives with fractional pantograph equations. Also, the fixed-point technique was used to evaluate the existence and uniqueness of solutions to the supposed hybrid model. Furthermore, stability results for the intended system in the sense of the Mittag-Leffler-Ulam have been investigated. Ultimately, an illustrative example has been highlighted in order to reinforce the theoretical results and suggest applications for this article.

Integral transforms involving a generalized k-Bessel function

Khammash Ghazi S., Salim Tariq O., Aydi Hassen, Khattab Noor N., Park Choonkil

Demonstratio Mathematica

2023

Vol. 56, nr 1

art. no. 20220246

The main goal of this study was to look into some new integral transformations that are associated with a generalized k-Bessel function. Integral formulas for the generalized k-Bessel function have been established using the Laplace transform, Euler transform, Whittaker transform, and k-transforms. The results presented here have the potential to be helpful, and some special cases of corollaries are explicitly demonstrated.