Browsing by Author "Elattar, Ehab E."

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Analytical results for positivity of discrete fractional operators with approximation of the domain of solutions
(Amer inst Mathematical Sciences-aims, 2022) Mohammed, Pshtiwan Othman; Baleanu, Dumitru; O'Regan, Donal; Baleanu, Dumitru; Hamed, Y. S.; Elattar, Ehab E.; 56389; Matematik
We study the monotonicity method to analyse nabla positivity for discrete fractional operators of Riemann-Liouville type based on exponential kernels, where ((CFR)(c0)del F-theta)(t) > -epsilon Lambda(theta - 1) (del F)(c(0) + 1) such that (del F)(c(0) + 1) >= 0 and epsilon > 0. Next, the positivity of the fully discrete fractional operator is analyzed, and the region of the solution is presented. Further, we consider numerical simulations to validate our theory. Finally, the region of the solution and the cardinality of the region are discussed via standard plots and heat map plots. The figures confirm the region of solutions for specific values of epsilon and theta.
Citation - WoS: 8
Citation - Scopus: 8
Positivity analysis for the discrete delta fractional differences of the Riemann-Liouville and Liouville-Caputo types
(Amer inst Mathematical Sciences-aims, 2022) Mohammed, Pshtiwan Othman; Baleanu, Dumitru; Srivastava, Hari Mohan; Baleanu, Dumitru; Elattar, Ehab E.; Hamed, Y. S.; 56389; Matematik
In this article, we investigate some new positivity and negativity results for some families of discrete delta fractional difference operators. A basic result is an identity which will prove to be a useful tool for establishing the main results. Our first main result considers the positivity and negativity of the discrete delta fractional difference operator of the Riemann-Liouville type under two main conditions. Similar results are then obtained for the discrete delta fractional difference operator of the Liouville-Caputo type. Finally, we provide a specific example in which the chosen function becomes nonincreasing on a time set.