Maximum and Minimum Results for the Green’s Functions in Delta Fractional Difference Settings
Pshtiwan Othman Mohammed,
Carlos Lizama,
Alina Alb Lupas,
Eman Al-Sarairah,
Mohamed Abdelwahed
Affiliations
Pshtiwan Othman Mohammed
Department of Mathematics, College of Education, University of Sulaimani, Sulaimani 46001, Iraq
Carlos Lizama
Departamento de Matemática y Ciencia de la Computación, Facultad de Ciencia, Universidad de Santiago de Chile, Casilla 307, Correo 2, Santiago 8320000, Chile
Alina Alb Lupas
Department of Mathematics and Computer Science, University of Oradea, 410087 Oradea, Romania
Eman Al-Sarairah
Department of Mathematics, Khalifa University of Science and Technology, Abu Dhabi P.O. Box 127788, United Arab Emirates
Mohamed Abdelwahed
Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
The present paper is dedicated to the examination of maximum and minimum results based on Green’s functions via delta fractional differences for a class of fractional boundary problems. For such a purpose, we built the corresponding Green’s functions based on the falling factorial functions. In addition, using the constructed Green’s function, the positivity of the function and its corresponding delta function are presented. We also verified the occurrence of two distinct functions with the same Green’s function. The maximality and minimality of the Green’s function show a good qualitative agreement. Finally, we considered some special examples to explain the obtained results.
