# Registered Data

Contents

- 1 [CT034]
- 1.1 [01083] The existence and the numerical approximation to a nonlinear coupled system in anisotropic Orlicz-Sobolev spaces
- 1.2 [02489] $L^p$-estimates for Maxwell's equations in heterogeneous materials
- 1.3 [00388] Numerical solution of distributed order time-fractional diffusion equations.
- 1.4 [00398] Approximation of Abel type nonlinear fractional integral equations by the use of orthogonal polynomials
- 1.5 [00991] Applied mathematics applications in ocean engineering

# [CT034]

## [01083] The existence and the numerical approximation to a nonlinear coupled system in anisotropic Orlicz-Sobolev spaces

**Session Date & Time**: 3C (Aug.23, 13:20-15:00)**Type**: Contributed Talk**Abstract**: We study the existence of a capacity solution for a nonlinear elliptic coupled system in anisotropic Orlicz-Sobolev spaces. The unknowns are the temperature inside a semiconductor material, and the electric potential. This system may be considered as a generalization of the steady-state thermistor problem. The numerical solution is also analyzed by means of the least squares method in combination with a conjugate gradient technique.**Classification**:__35J70__,__35J66__,__35K61__,__46E30__,__65N22__**Author(s)**:**Hakima Ouyahya**(Moulay Ismail University)

## [02489] $L^p$-estimates for Maxwell's equations in heterogeneous materials

**Session Date & Time**: 3C (Aug.23, 13:20-15:00)**Type**: Contributed Talk**Abstract**: Estimates for the time-harmonic Maxwell's equations in heterogeneous materials are concerned. The materials contain two constituents. One high-conductivity constituent of small size is embedded in each period so that it is disconnected. The other of low-conductivity constituent contains the rest of the material. The contrast ratios of the conductivity and the magnetic permeability in one constituent to the other can be very high. Here $L^p$-estimates for the electromagnetic fields uniform in contrast ratios are presented.**Classification**:__35J70__,__35J25__,__35J75__**Author(s)**:**Li-Ming Yeh**(National Yang Ming Chiao Tung University)- Dongwoo Sheen (Seoul National University)

## [00388] Numerical solution of distributed order time-fractional diffusion equations.

**Session Date & Time**: 3C (Aug.23, 13:20-15:00)**Type**: Contributed Talk**Abstract**: In this work, we solved distributed order time-fractional diffusion equation with the help of a wavelet approximation scheme and the Gauss quadrature rule. First, we construct wavelet-based operational matrices of distributed order fractional derivatives and integer order derivatives. After the construction of the operational matrix apply the tau method and convert the original mathematical problem into a system of linear algebraic equations and solve the equations for finding the approximate solutions. For method validation, we have provided some test examples, convergence analysis, and error estimation, and verify with the existing scheme with one of the existing schemes.**Classification**:__35J99__,__65N35__,__65N99__**Author(s)**:**Yashveer Kumar**(Indian Institute of Technology(BHU), Varanasi, India.)- Vineet Kumar Singh (Department of Mathematical Sciences, Indian Institute of Technology (Banaras Hindu University), Varanasi, India.)

## [00398] Approximation of Abel type nonlinear fractional integral equations by the use of orthogonal polynomials

**Session Date & Time**: 3C (Aug.23, 13:20-15:00)**Type**: Contributed Talk**Abstract**: The nonlinear fractional integral equations of the type Abel are presented in this study with general framework for determining the approximate solution. As basis functions, this method makes use of Lagrangian interpolating polynomials (LIPs) and shifting Legendre polynomials (SLPs). The original problem is converted into a system of algebraic nonlinear equations using operational matrices of SLPs and LIPs, which are first developed. We investigated at the provided techniques' stability and convergence under several significant conditions.**Classification**:__35J99__,__65N35__,__65N99__**Author(s)**:**Aman Singh**(Department of Mathematical Sciences, Indian Institute of Technology (Banaras Hindu University))- Vineet Kumar Singh (Department of Mathematical Sciences, Indian Institute of Technology (Banaras Hindu University))

## [00991] Applied mathematics applications in ocean engineering

**Session Date & Time**: 3C (Aug.23, 13:20-15:00)**Type**: Industrial Contributed Talk**Abstract**: A novel controller technique using nonlinear quadratic regulatory framework is proposed, the algorithm perform the parameterization of the nonlinear model of the system such that the linearized model remains transversal everywhere to nonlinear model leading to control of original model. By transversality, linearized and nonlinear solutions intersect at only grid points on time axis without using Taylor-like expansions and shown its applicability in SWT**Classification**:__37D10__**Author(s)**:**MANIKANDAN RAJASEKARAN**(UGC-DR DS KOTHARI POST DOCTORAL FELLOW DEPARTMENT OF APPLIED MATHEMATICS BHARATHIYAR UNIVERSITY COIMBATORE TAMIL NADU INDIA)- SATARUPA DEY (Assistant Professor and Head Department of Botany Shyampur Siddheswari Mahavidyalaya (Affiliated to University of Calcutta) West Bengal India)
- SAKTHIVEL R (DEPARTMENT OF APPLIED MATHEMATICS BHARATHIYAR UNIVERSITY COIMBATORE TAMIL NADU INDIA)