Browsing by Subject "monotone method"

Now showing 1 - 4 of 4

Access status: Open Access ,
Existence of minimal and maximal solutions to RL fractional integro-differential initial value problems
(Wydawnictwa AGH, 2017) Denton Zachary; Ramírez, J.D.
In this work we investigate integro-differential initial value problems with Riemann Liouville fractional derivatives where the forcing function is a sum of an increasing function and a decreasing function. We will apply the method of lower and upper solutions and develop two monotone iterative techniques by constructing two sequences that converge uniformly and monotonically to minimal and maximal solutions. In the first theorem we will construct two natural sequences and in the second theorem we will construct two intertwined sequences. Finally, we illustrate our results with an example.
Access status: Restricted ,
Istnienie i jednoznaczność rozwiązania klasycznego układu ewolucyjnych równań różniczkowych
(Data obrony: 2017-07-10) Światłowska, Julita
Wydział Matematyki Stosowanej
Access status: Open Access ,
Monotone iterative technique for fractional differential equations with periodic boundary conditions
(2009) Ramirez, J. D.; Vatsala, A. S.
In this paper we develop Monotone Method using upper and lower solutions for fractional differential equations with periodic boundary conditions. Initially we develop a comparison result and prove that the solution of the linear fractional differential equation with periodic boundary condition exists and is unique. Using this we develop iterates which converge uniformly monotonically to minimal and maximal solutions of the nonlinear fractional differential equations with periodic boundary conditions in the weighted norm.
Access status: Open Access ,
Monotone method for Riemann-Liouville multi-order fractional differential systems
(2016) Denton, Zachary
In this paper we develop the monotone method for nonlinear multi-order $N$-systems of Riemann-Liouville fractional differential equations. That is, a hybrid system of nonlinear equations of orders $q_i$ where $0 \lt q_i \lt 1$. In the development of this method we recall any needed existence results along with any necessary changes. Through the method's development we construct a generalized multi-order Mittag-Leffler function that fulfills exponential-like properties for multi-order systems. Further we prove a comparison result paramount for the discussion of fractional multi-order inequalities that utilizes lower and upper solutions of the system. The monotone method is then developed via the construction of sequences of linear systems based on the upper and lower solutions, and are used to approximate the solution of the original nonlinear multi-order system.