Computational approach based on wavelets for financial mathematical model governed by distributed order fractional differential equation

2021 ◽  
Author(s):  
Yashveer Kumar ◽  
Vineet Kumar Singh
Keyword(s):  
Differential Equation ◽  
Mathematical Model ◽  
Fractional Differential Equation ◽  
Computational Approach ◽  
Fractional Differential ◽  
Distributed Order

scholarly journals A computational approach for solving time fractional differential equation via spline functions

2020 ◽  
Vol 59 (5) ◽  
pp. 3061-3078 ◽  
Author(s):  
Nauman Khalid ◽  
Muhammad Abbas ◽  
Muhammad Kashif Iqbal ◽  
Jagdev Singh ◽  
Ahmad Izani Md. Ismail
Keyword(s):  
Differential Equation ◽  
Fractional Differential Equation ◽  
Computational Approach ◽  
Spline Functions ◽  
Fractional Differential

scholarly journals Fractional Differential Equation-Based Instantaneous Frequency Estimation for Signal Reconstruction

2021 ◽  
Vol 5 (3) ◽  
pp. 83
Author(s):  
Bilgi Görkem Yazgaç ◽  
Mürvet Kırcı
Keyword(s):  
Differential Equation ◽  
Fractional Differential Equation ◽  
Frequency Estimation ◽  
Signal Reconstruction ◽  
Reconstruction Method ◽  
Reconstruction Algorithms ◽  
Instantaneous Frequency Estimation ◽  
Proposed Model ◽  
Fractional Differential ◽  
Instantaneous Frequencies

In this paper, we propose a fractional differential equation (FDE)-based approach for the estimation of instantaneous frequencies for windowed signals as a part of signal reconstruction. This approach is based on modeling bandpass filter results around the peaks of a windowed signal as fractional differential equations and linking differ-integrator parameters, thereby determining the long-range dependence on estimated instantaneous frequencies. We investigated the performance of the proposed approach with two evaluation measures and compared it to a benchmark noniterative signal reconstruction method (SPSI). The comparison was provided with different overlap parameters to investigate the performance of the proposed model concerning resolution. An additional comparison was provided by applying the proposed method and benchmark method outputs to iterative signal reconstruction algorithms. The proposed FDE method received better evaluation results in high resolution for the noniterative case and comparable results with SPSI with an increasing iteration number of iterative methods, regardless of the overlap parameter.

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