Hyers-Ulam-Rassias-Kummer stability of the fractional integro-differential equations
Zahra Eidinejad1, Reza Saadati1
1School of Mathematics, Iran University of Science and Technology, Narmak, Tehran 13114-16846, Iran.
Abstract:
In this paper, using the fractional integral with respect to the Ψ function and the Ψ-Hilfer fractional derivative, we consider the Volterra fractional equations. Considering the Gauss Hypergeometric function as a control function, we introduce the concept of the Hyers-Ulam-Rassias-Kummer stability of this fractional equations and study existence, uniqueness, and an approximation for two classes of fractional Volterra integro-differential and fractional Volterra integral. We apply the Cădariu-Radu method derived from the Diaz-Margolis alternative fixed point theorem. After proving each of the main theorems, we provide an applied example of each of the results obtained.
More Related Videos
12:21Stimulated Stokes and Antistokes Raman Scattering in Microspherical Whispering Gallery Mode Resonators
Published on: April 4, 2016
11:38Combining Microfluidics and Microrheology to Determine Rheological Properties of Soft Matter during Repeated Phase Transitions
Published on: April 19, 2018
Related Concept Videos
Routh-Hurwitz Criterion II
The first scenario occurs when a singular zero appears in the first column of the Routh table. This situation creates a division by zero issues. To resolve this, a small positive or negative number, denoted as epsilon (∈), is substituted for the zero. The stability analysis proceeds by assuming a sign for ∈. If ∈ is positive, any sign change in the first...
RLC Circuit as a Damped Oscillator
Consider a series RLC circuit. Here, the presence of resistance in the circuit leads to energy loss due to joule heating in the resistance. Therefore, the total electromagnetic energy in the circuit is no longer constant and decreases with time. Since the magnitude of charge, current, and potential difference continuously decreases, their oscillations are said to be damped. This is...
Pole and System Stability
Simple poles are unique roots of the denominator polynomial. Each simple pole corresponds to a distinct solution to the system's characteristic equation, typically resulting in exponential decay terms in the system's...
Routh-Hurwitz Criterion I
To apply the Routh-Hurwitz criterion, a Routh table is constructed. The table's rows are labeled with powers of the complex frequency variable s, starting from the...
Linear Approximation in Frequency Domain
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
Second Order systems II
