# Registered Data

Contents

- 1 [CT018]
- 1.1 [00326] Estimating the lowest-order eigenvalue in Sturm-Liouville boundary value problem
- 1.2 [01392] Solving a fractional pantograph delay equation
- 1.3 [00566] Numerical study of Draw resonance in Fibre spinning using multi-mode constitutive model
- 1.4 [01345] Novel Lyapunov-type Inequality Involving Riesz Fractional Derivative
- 1.5 [00034] Relative heat flux in nonlocal reaction-diffusion equations and thermoelectric efficiency

# [CT018]

## [00326] Estimating the lowest-order eigenvalue in Sturm-Liouville boundary value problem

**Session Date & Time**: 4E (Aug.24, 17:40-19:20)**Type**: Contributed Talk**Abstract**: We investigate a special case of the Sturm–Liouville boundary value problem $($BVP$)$ and examine the BVP in the Schrödinger form. By considering a reciprocal quadratic form of the corresponding invariant function, we estimate the lowest-order eigenvalue without solving the eigenvalue problem but by utilizing the localized landscape and effective potential functions. Some combinations of parameter values yield poor spectrum estimates. Other combinations are satisfactorily although the values tend to overestimate results from numerical computations.**Classification**:__34B05__,__34B24__,__34L15__**Author(s)**:**Natanael Karjanto**(Sungkyunkwan University)

## [01392] Solving a fractional pantograph delay equation

**Session Date & Time**: 4E (Aug.24, 17:40-19:20)**Type**: Contributed Talk**Abstract**: We study a pantograph delay equation involving a fractional derivative. Our approach relies basically on the reduction of the considered problem to an equivalent integral equation, then by using fixed point theorems, we prove the existence results. We also discussed the fractional Ambartsumian differential equation, that describes in the classical case the absorption of light by the interstellar matter.**Classification**:__34B05__,__26A33__,__34A30__**Author(s)**:**Assia Guezane Laakoud**(Badji Mokhtar Annaba University)- Rabah Khaldi (Badji Mokhtar Annaba University)

## [00566] Numerical study of Draw resonance in Fibre spinning using multi-mode constitutive model

**Session Date & Time**: 4E (Aug.24, 17:40-19:20)**Type**: Contributed Talk**Abstract**: We study the instability called Draw resonance that occurs in the industrial process of manufacture of thin polymer fibres, called fibre spinning using a multi-mode viscoelastic constitutive equation. We do a linear stability analysis of the equations by carrying out numerical simulations for a varying number of modes in the constitutive equation. We compare our results with those got by using single-mode viscoelastic models and discuss our findings.**Classification**:__34B09__,__34B60__,__65N25__,__Polymer flows in industrial processes__**Author(s)**:**Renu Dhadwal**(Center for Mathematical Modelling, FLAME University )

## [01345] Novel Lyapunov-type Inequality Involving Riesz Fractional Derivative

**Session Date & Time**: 4E (Aug.24, 17:40-19:20)**Type**: Contributed Talk**Abstract**: In this work, we obtained necessary condition for the existence of solutions to a fractional boundary value problem involving Riesz fractional derivative, which is defined as a two-sided fractional operator. The approach proposed in this work is based on the reduction of the problem considered to a singular integral equation, then we derive the Lyapunov-type inequalities in a weighted Lebesgue space.**Classification**:__34B10__,__34B16__,__34B18__**Author(s)**:**Rabah Khaldi**(Badji Mokhtar Annaba University)- Assia Guezane Laakoud (Badji Mokhtar Annaba University)

## [00034] Relative heat flux in nonlocal reaction-diffusion equations and thermoelectric efficiency

**Session Date & Time**: 4E (Aug.24, 17:40-19:20)**Type**: Contributed Talk**Abstract**: Thermoelectric generators directly convert a temperature difference into electrical energy. To study their efficiency, we consider second-order integro-differential equations describing the steady-state temperature distribution inside thermoelectric generators when the Seebeck coefficient of the thermoelectric material is temperature-independent but the electrical resistivity and thermal conductivity are temperature-dependent. In this talk, we show that the temperature solution is unique and the relative boundary Fourier heat flux can be explicitly written. Therefore, the efficiency has an explicit formula.**Classification**:__34B15__,__35A02__,__35J25__,__34B10__,__35K59__**Author(s)**:**Jaywan Chung**(Korea Electrotechnology Research Institute)- Byungki Ryu (Korea Electrotechnology Research Institute)
- Hyowon Seo (Kunsan National University)