scholarly journals Asymptotic Periodicity for a Class of Partial Integrodifferential Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-18 ◽  
Author(s):  
Alejandro Caicedo ◽  
Claudio Cuevas ◽  
Hernán R. Henríquez
Keyword(s):  
Heat Conduction ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Integral Equations ◽  
Integrodifferential Equations ◽  
Materials With Memory ◽  
Asymptotic Periodicity ◽  
With Memory ◽  
Equations With Delay

We study the existence of S-asymptotically ω-periodic solutions for a class of abstract partial integro-differential equations and for a class of abstract partial integrodifferential equations with delay. Applications to integral equations arising in the study of heat conduction in materials with memory are shown.

Periodic solutions of differential equations with delay depending on solution

1997 ◽  
Vol 30 (5) ◽  
pp. 2665-2672 ◽  
Author(s):  
Alexander Domoshnitsky ◽  
Michael Drakhlin
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Equations With Delay

scholarly journals Specific Mathematical Aspects of Dynamics Generated by Coherence Functions

2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
Ezzat G. Bakhoum ◽  
Cristian Toma
Keyword(s):  
Differential Equations ◽  
Complex Systems ◽  
Integral Equations ◽  
Quantum Physics ◽  
Initial Conditions ◽  
Coherence Function ◽  
Multiple Integral ◽  
The State ◽  
Integrodifferential Equations ◽  
State Variables

This study presents specific aspects of dynamics generated by the coherence function (acting in an integral manner). It is considered that an oscillating system starting to work from initial nonzero conditions is commanded by the coherence function between the output of the system and an alternating function of a certain frequency. For different initial conditions, the evolution of the system is analyzed. The equivalence between integrodifferential equations and integral equations implying the same number of state variables is investigated; it is shown that integro-differential equations of second order are far more restrictive regarding the initial conditions for the state variables. Then, the analysis is extended to equations of evolution where the coherence function is acting under the form of a multiple integral. It is shown that for the coherence function represented under the form of annth integral, some specific aspects as multiscale behaviour suitable for modelling transitions in complex systems (e.g., quantum physics) could be noticed whennequals 4, 5, or 6.

scholarly journals Properties for ψ-Fractional Integrals Involving a General Function ψ and Applications

Mathematics ◽  
2019 ◽  
Vol 7 (6) ◽  
pp. 517
Author(s):  
Jin Liang ◽  
Yunyi Mu
Keyword(s):  
Differential Equations ◽  
Integral Equations ◽  
Fractional Differential Equations ◽  
Fractional Integral ◽  
Integrodifferential Equations ◽  
Fractional Integrals ◽  
General Function ◽  
Fractional Differential ◽  
Hadamard Fractional Integrals

In this paper, we are concerned with the ψ-fractional integrals, which is a generalization of the well-known Riemann–Liouville fractional integrals and the Hadamard fractional integrals, and are useful in the study of various fractional integral equations, fractional differential equations, and fractional integrodifferential equations. Our main goal is to present some new properties for ψ-fractional integrals involving a general function ψ by establishing several new equalities for the ψ-fractional integrals. We also give two applications of our new equalities.

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