Wyniki wyszukiwania - BazTech

Ograniczanie wyników

3 Opuscula Mathematica

Znaleziono wyników: 3

Liczba wyników na stronie

Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

Existence of minimal and maximal solutions to RL fractional integro-differential initial value problems

Denton Z., Ramirez J. D.

Opuscula Mathematica

2017

Vol. 37, no. 5

705--724

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.

Monotone method for Riemann-Liouville multi-order fractional differential systems

Denton Z.

Opuscula Mathematica

2016

Vol. 36, no. 2

189--206

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 qi where 0 < qi < 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.

Monotone iterative technique for finite systems of nonlinear Riemann-,Lliouville fractional differential equations

Denton Z., Vatsala A.S.

Opuscula Mathematica

2011

Vol. 31, no. 3

327-339

Comparison results of the nonlinear scalar Riemann-Liouville fractional differential equation of order q, 0 < q ≤ 1, are presented without requiring Hölder continuity assumption. Monotone method is developed for finite systems of fractional differential equations of order q, using coupled upper and lower solutions. Existence of minimal and maximal solutions of the nonlinear fractional differential system is proved.