Existence and stability results on multidimensional fractional-order systems (original) (raw)

Analysis of Fractional Differential Equations with Multi-Orders

Fractals, 2007

In this paper, we study two kinds of fractional differential systems with multi-orders. One is a system of fractional differential equations with multi-order, [Formula: see text], [Formula: see text]; the other is a multi-order fractional differential equation, [Formula: see text]. By the derived technique, such two kinds of fractional differential equations can be changed into equations with the same fractional orders providing that the multi-orders are rational numbers, so the known theorems of existence, uniqueness and dependence upon initial conditions are easily applied. And asymptotic stability theorems for their associate linear systems, [Formula: see text], [Formula: see text], and [Formula: see text], [Formula: see text], [Formula: see text], are also derived.

Hyers–Ulam’s Stability Results to a Three-Point Boundary Value Problem of Nonlinear Fractional Order Differential Equations

Frontiers in Functional Equations and Analytic Inequalities, 2019

This research is devoted to investigate the existence and multiplicity results of boundary value problem (BVP) for nonlinear fractional order differential equation (FDEs). To obtain the required results, we use some fixed point theorems due to Leggett–Williams and Banach. Further in this paper, we introduce different types of Ulam’s stability concepts for the aforesaid problem of nonlinear FDEs. The concerned types of Ulam’s stability are devoted to Ulam–Hyers (UH), generalized Ulam–Hyers (GUH) stability and Ulam–Hyers–Rassias (UHR), generalized Ulam–Hyers–Rassias (GUHR) stability. Finally the whole analysis is verified by some adequate examples.

Ulam–Hyers–Mittag-Leffler stability for tripled system of weighted fractional operator with TIME delay

Advances in Difference Equations, 2021

This study is aimed to investigate the sufficient conditions of the existence of unique solutions and the Ulam–Hyers–Mittag-Leffler (UHML) stability for a tripled system of weighted generalized Caputo fractional derivatives investigated by Jarad et al. (Fractals 28:2040011 2020) in the frame of Chebyshev and Bielecki norms with time delay. The acquired results are obtained by using Banach fixed point theorems and the Picard operator (PO) method. Finally, a pertinent example of the results obtained is demonstrated.

Existence and Stability Analysis of Sequential Coupled System of Hadamard-Type Fractional Differential Equations

Kragujevac Journal of Mathematics, 2022

In this paper we study existence, uniqueness and Hyers-Ulam stability for a sequential coupled system consisting of fractional differential equations of Hadamard type, subject to nonlocal Hadamard fractional integral boundary conditions. The existence of solutions is derived from Leray-Schauder’s alternative, whereas the uniqueness of solution is established by Banach contraction principle. An example is also presented which illustrate our results.