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Existence, uniqueness and parameter perturbation analysis results of a fractional integro-differential boundary problem

Zhang Nan, Zhang Lingling, Ngungu Mercy, Adeniji Adejimi, Addai Emmanuel

Bulletin of the Polish Academy of Sciences. Technical Sciences

2023

Vol. 71, nr 4

art. no. e145938

In the formulation, the existence, uniqueness and stability of solutions and parameter perturbation analysis to Riemann-Liouville fractional differential equations with integro-differential boundary conditions are discussed by the properties of Green’s function and cone theory. First, some theorems have been established from standard fixed point theorems in a proper Banach space to guarantee the existence and uniqueness of positive solution. Moreover, we discuss the Hyers-Ulam stability and parameter perturbation analysis, which examines the stability of solutions in the presence of small changes in the equation main parameters, that is, the derivative order η, the integral order β of the boundary condition, the boundary parameter ξ , and the boundary value τ. As an application, we present a concrete example to demonstrate the accuracy and usefulness of the proposed work. By using numerical simulation, we obtain the figure of unique solution and change trend figure of the unique solution with small disturbances to occur in different kinds of parameters.

Comparison ODE theorems related to the method of lines

Leszczyński H.

Journal of Applied Analysis

2011

Vol. 17, nr 1

137-154

We prove a comparison theorem for an ODE and DAE system which arises from the method of lines. Under a Perron comparison condition on the functional dependence and a specific Lipschitz and (W+) condition on the classical argument, we obtain strong uniqueness criteria.

O osobliwych rozwiązaniach zagadnienia n ciał

Strzelecki P.

Postępy Fizyki

2005

T. 56, z. 2

50-56

We discuss some of the mathematical features of the n-body problem and give a popular account of Xia's construction of noncollision singularities for n > 4.