On a new structure of multi-term Hilfer fractional impulsive neutral Levin-Nohel integrodifferential system with variable time delay

Thabet Abdeljawad, Sabri T.M. Thabet, Imed Kedim, Miguel Vivas-Cortez

• Facultad de Ciencias Exactas y Naturales
• 
  

Resumen

The Levin-Nohel equations play key roles in the interpretation of real phenomena and have interesting applications in engineering and science areas, such as mathematical physics, mathematical biology, image processing, and numerical analyses. This article investigates a new structure for the delay neutral Levin-Nohel integrodifferential (NLNID) system via a Hilfer fractional derivative and is supplemented by initial and instantaneous impulse conditions. A fractional integral equation corresponding to the proposed system is derived and used to prove the existence and uniqueness of the solution with the help of the Banach contraction principle. Additionally, the Ulam-Hyers-MittagLeffler (UHML) stability is studied by utilizing the generalized Gronwall’s inequality and nonlinear analysis issues. As a consequence, the Ulam-Hyers (UH) stability and generalized UH are also deduced. Furthermore, the Riemann-Liouville (R.L.) and Caputo fractional versions of the proposed system are discussed. Finally, numerical applications supported with tables and graphics are provided to test the exactitude of the findings.

Idioma original	Inglés
Páginas (desde-hasta)	7372-7395
Número de páginas	24
Publicación	AIMS Mathematics
Volumen	9
N.º	3
Estado	Publicada - 2024

Nota bibliográfica

Publisher Copyright:
© 2024 the Author(s), licensee AIMS Press.

https://www.aimspress.com/article/doi/10.3934/math.2024357

 

New results about fuzzy γ-convex functions connected with the q-analogue multiplier-Noor integral operator

Ekram E. Ali, Miguel Vivas-Cortez, Rabha M. El-Ashwah

• Facultad de Ciencias Exactas y Naturales

• Resumen

  The features of analytical functions were mostly studied using a fuzzy subset and a q-difference operator in this study, as we investigate many fuzzy differential subordinations related to the q-analogue multiplier-Noor integral operator. By applying fuzzy subordination to univalent functions whose range is symmetric with respect to the real axis, we create a few new subclasses of analytical functions. We define numerous classes related to the family of linear q-operators and introduce them. Here, we focus on the inclusion results and other integral features.

  Idioma original	Inglés
  Páginas (desde-hasta)	5451-5465
  Número de páginas	15
  Publicación	AIMS Mathematics
  Volumen	9
  N.º	3
  Estado	Publicada - 2024

  Nota bibliográfica

  Publisher Copyright:
  © 2024 the Author(s).
• https://www.aimspress.com/article/doi/10.3934/math.2024263
  

 

A STUDY of FRACTIONAL HERMITE-HADAMARD-MERCER INEQUALITIES for DIFFERENTIABLE FUNCTIONS

Thanin Sitthiwirattham, Miguel Vivas-Cortez, Muhammad Aamir Ali, Hüseyin Budak, Ibrahim Avci

Resumen

In this work, we prove a parameterized fractional integral identity involving differentiable functions. Then, we use the newly established identity to establish some new parameterized fractional Hermite-Hadamard-Mercer-Type inequalities for differentiable function. The main benefit of the newly established inequalities is that these inequalities can be converted into some new Mercer inequalities of midpoint type, trapezoidal type, and Simpson's type for differentiable functions. Finally, we show the validation of the results with the help of some mathematical examples and their graphs.

Idioma original	Inglés
Número de artículo	2440016
Publicación	Fractals
Estado	Aceptada/en prensa - 2024

Nota bibliográfica

Publisher Copyright:
© 2024 World Scientific Publishing Co. Pte Ltd. All rights reserved.

https://www.worldscientific.com/doi/10.1142/S0218348X24400164