The Neumann problem for the generalized Bagley-Torvik fractional differential equation

2016 ◽  
Vol 19 (4) ◽  
Author(s):  
Svatoslav Staněk
Keyword(s):  
Differential Equation ◽  
Neumann Problem ◽  
Fractional Differential Equation ◽  
Multiplicity Of Solutions ◽  
Existence And Multiplicity ◽  
Fractional Differential ◽  
The Neumann Problem

AbstractWe discuss the existence and multiplicity of solutions to the generalized Bagley-Torvik fractional differential equation

Multiplicity Results for Integral Boundary Value Problems of Fractional Order with Parametric Dependence

2015 ◽  
Vol 18 (1) ◽  
Author(s):  
Alberto Cabada ◽  
Zakaria Hamdi
Keyword(s):  
Differential Equation ◽  
Fractional Differential Equation ◽  
Boundary Value ◽  
Nonlinear Fractional Differential Equation ◽  
Integral Boundary ◽  
Multiplicity Results ◽  
Parametric Dependence ◽  
Existence And Multiplicity ◽  
Fractional Differential ◽  
Integral Boundary Value Problems

AbstractThis paper is devoted to the study of nonlinear fractional differential equation with parameter dependence and integral boundary value conditions. In the paper various existence and multiplicity results for positive solutions are derived depending of different values of the parameter. Some illustrative examples are also discussed.

scholarly journals Existence of Concave Positive Solutions for Boundary Value Problem of Nonlinear Fractional Differential Equation withp-Laplacian Operator

2010 ◽  
Vol 2010 ◽  
pp. 1-17 ◽  
Author(s):  
Jinhua Wang ◽  
Hongjun Xiang ◽  
ZhiGang Liu
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Boundary Value Problem ◽  
Fractional Differential Equation ◽  
Positive Solutions ◽  
Boundary Value ◽  
Laplacian Operator ◽  
Nonlinear Fractional Differential Equation ◽  
Existence And Multiplicity ◽  
Fractional Differential

We consider the existence and multiplicity of concave positive solutions for boundary value problem of nonlinear fractional differential equation withp-Laplacian operatorD0+γ(ϕp(D0+αu(t)))+f(t,u(t),D0+ρu(t))=0,0<t<1,u(0)=u′(1)=0,u′′(0)=0,D0+αu(t)|t=0=0, where0<γ<1,2<α<3,0<ρ⩽1,D0+αdenotes the Caputo derivative, andf:[0,1]×[0,+∞)×R→[0,+∞)is continuous function,ϕp(s)=|s|p-2s,p>1,  (ϕp)-1=ϕq,  1/p+1/q=1. By using fixed point theorem, the results for existence and multiplicity of concave positive solutions to the above boundary value problem are obtained. Finally, an example is given to show the effectiveness of our works.

scholarly journals Monotone and Concave Positive Solutions to a Boundary Value Problem for Higher-Order Fractional Differential Equation

2011 ◽  
Vol 2011 ◽  
pp. 1-14 ◽  
Author(s):  
Jinhua Wang ◽  
Hongjun Xiang ◽  
Yuling Zhao
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Fractional Differential Equation ◽  
Boundary Value ◽  
Higher Order ◽  
Fractional Boundary Value Problem ◽  
Interesting Point ◽  
Nonlinear Fractional Differential Equation ◽  
Existence And Multiplicity ◽  
Fractional Differential

We consider boundary value problem for nonlinear fractional differential equationD0+αu(t)+f(t,u(t))=0,  0<t<1,  n-1<α≤n,  n>3,  u(0)=u'(1)=u′′(0)=⋯=u(n-1)(0)=0, whereD0+αdenotes the Caputo fractional derivative. By using fixed point theorem, we obtain some new results for the existence and multiplicity of solutions to a higher-order fractional boundary value problem. The interesting point lies in the fact that the solutions here are positive, monotone, and concave.

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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