# Registered Data

Contents

- 1 [CT059]
- 1.1 [00834] Analytical Solution for Linearized Diffusive Wave with Concentrated Lateral Inflow
- 1.2 [02594] Two-dimensional fractional Stockwell transform on quaternion valued functions and its applications
- 1.3 [01844] Operational Matrix Based Numerical Scheme for Fractional Differential Equations
- 1.4 [02046] Applications to give an analytical solution to the Black Scholes equation
- 1.5 [00896] Error analysis of Jacobi modified projection-type method for weakly singular Volterra–Hammerstein integral equations

# [CT059]

## [00834] Analytical Solution for Linearized Diffusive Wave with Concentrated Lateral Inflow

**Session Date & Time**: 4E (Aug.24, 17:40-19:20)**Type**: Contributed Talk**Abstract**: We present a solution for flow depth and discharge at different locations of a finite prismatic channel for linearized diffusive wave approximation with concentrated lateral inflow subjected to water discharge as the upstream boundary and flow depth as the downstream boundary. Laplace transform is used to find the analytical solution. We present some results to show the effect of Peclet number and the point of confluence on discharge and flow depth.**Classification**:__44A10__,__35Q35__,__86A05__,__Hydraulics, River Mechanics__**Author(s)**:**Shiva Kandpal**(Indian Institute of Technology Guwahati)- Swaroop Nandan Bora (Indian Institute of Technology Guwahati)

## [02594] Two-dimensional fractional Stockwell transform on quaternion valued functions and its applications

**Session Date & Time**: 4E (Aug.24, 17:40-19:20)**Type**: Contributed Talk**Abstract**: We define a two-dimension fractional Stockwell transform on $L^2(\mathbb{R}^2,\mathbb{H})$ using the quaternionic fractional convolution and derive the properties of the transform such as Parseval's identity, inversion formula. As color images can be viewed as elements of $L^2(\mathbb{R}^2,\mathbb{H})$, we can apply this quaternionic integral transform for processing color images.**Classification**:__44A35__,__44A15__,__46S10__**Author(s)**:**Roopkumar Rajakumar**(Central University of Tamil Nadu)

## [01844] Operational Matrix Based Numerical Scheme for Fractional Differential Equations

**Session Date & Time**: 4E (Aug.24, 17:40-19:20)**Type**: Contributed Talk**Abstract**: Fractional calculus is active in many engineering and physics disciplines due to their non-local properties. This non integer order derivative performs well in systems where the next state depends not only on the current state but also upon all of its previous states. Modeling such systems and determining their precise solutions are current research topics of interest. Since finding exact solutions for fractional differential equations is more challenging, developing numerical techniques is a trending research topic. In this paper, we propose the spectral collocation method based on the operational matrix of orthogonal basis polynomials to find the approximate solution of fractional differential equations. Different orthogonal and non orthogonal basis polynomials are considered for the approximation, and a comparative study is made. The operational matrix of fractional order derivatives of basis polynomials is derived as a product of matrices. This matrix together with the collocation method, is employed to transform the fractional differential equations into a set of algebraic equations, which is easier to tackle. The perturbation method is applied to show the stability of the discussed method. The solution achieved by this method is more precise than those obtained from the existing methods like the variational iterational, adomian decomposition method, and finite difference method.**Classification**:__44Axx__,__33C50__,__65N35__,__Fractional Calculus__**Author(s)**:- Ashish Awasthi (National Institute of Technology Calicut)
**Poojitha S**(National Institute of Technology Calicut)

## [02046] Applications to give an analytical solution to the Black Scholes equation

**Session Date & Time**: 4E (Aug.24, 17:40-19:20)**Type**: Contributed Talk**Abstract**: A simple ℵ-function and its dynamic equation is presented. An application to give an analytical solution to the Black Scholes equation is presented. A probability distribution hasn’t got a price unit, thus it never can be bought. Only the expectation value, the square root of the variance, and the cubic root of the asymmetry have got a price unit and should all three be considered, when hedging stock prices realistically.**Classification**:__44Axx__,__35Qxx__,__35A24__,__26A33__,__35Q84__**Author(s)**:**Dinesh Kumar**(Agriculture University Jodhpur)- Nobert Sudland (Aage GmbH, Rontgenstraße, Aalen)
- Jorg Volkmann (International Laboratory of Theoretical Physics, Bashkir State Pedagogical University, Ufa)

## [00896] Error analysis of Jacobi modified projection-type method for weakly singular Volterra–Hammerstein integral equations

**Session Date & Time**: 4E (Aug.24, 17:40-19:20)**Type**: Contributed Talk**Abstract**: In this paper, polynomially based projection-type and modified projection-type methods are developed for weakly singular Volterra-Hammerstein integral equations of the second kind, using Jacobi polynomials as basis functions. In general, this type of equations has a singular behavior at the left endpoint of the interval of integration with exact solutions being typically nonsmooth. In the considered approach a transformation of the independent variable is first introduced in order to find a new integral equation with a smoother solution, so that the Jacobi spectral method can be applied conveniently to the transformed equation and a complete convergence analysis of the method is carried. The effectiveness of the proposed approach is illustrated through different numerical tests.**Classification**:__45D05__,__45A05__,__65R20__,__Approximation of Integral Equations__**Author(s)**:**Kapil Kant**(Indian Institute of Technology Kanpur)