Approximate Controllability for a Class of Non-instantaneous Impulsive Stochastic Fractional Differential Equation Driven by Fractional Brownian Motion

2019 ◽  
Author(s):  
Rajesh Dhayal ◽  
Muslim Malik ◽  
Syed Abbas
Keyword(s):  
Differential Equation ◽  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Fractional Differential Equation ◽  
Approximate Controllability ◽  
Stochastic Fractional Differential Equation ◽  
Fractional Differential

scholarly journals Cauchy Problem for a Stochastic Fractional Differential Equation with Caputo-Itô Derivative

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1479
Author(s):  
Jorge Sanchez-Ortiz ◽  
Omar U. Lopez-Cresencio ◽  
Francisco J. Ariza-Hernandez ◽  
Martin P. Arciga-Alejandre
Keyword(s):  
Differential Equation ◽  
Cauchy Problem ◽  
Fractional Differential Equation ◽  
Existence And Uniqueness ◽  
Contraction Mapping ◽  
Stochastic Fractional Differential Equation ◽  
Fractional Differential

In this note, we define an operator on a space of Itô processes, which we call Caputo-Itô derivative, then we considerer a Cauchy problem for a stochastic fractional differential equation with this derivative. We demonstrate the existence and uniqueness by a contraction mapping argument and some examples are given.

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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