scholarly journals On a fractional hybrid integro-differential equation with mixed hybrid integral boundary value conditions by using three operators

2020 ◽  
Vol 59 (5) ◽  
pp. 3019-3027 ◽  
Author(s):  
D. Baleanu ◽  
S. Etemad ◽  
Sh. Rezapour
Keyword(s):  
Differential Equation ◽  
Boundary Value ◽  
Integral Boundary ◽  
Integro Differential Equation ◽  
Hybrid Integral

ON AN INTEGRO-DIFFERENTIAL EQUATION OF PSEUDOPARABOLIC-PSEUDOHYPERBOLIC TYPE WITH DEGENERATE KERNELS

2018 ◽  
Vol 52 (1 (245)) ◽  
pp. 19-26 ◽  
Author(s):  
T.K. Yuldashev
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Separation Of Variables ◽  
Boundary Value ◽  
Fourier Method ◽  
Integro Differential Equation ◽  
The One

In the article the questions of solvability of boundary value problem for a homogeneous pseudoparabolic-pseudohyperbolic type integro-differential equation with degenerate kernels are considered. The Fourier method based on separation of variables is used. A criterion for the one-valued solvability of the considering problem is found. Under this criterion the one-valued solvability of the problem is proved.

scholarly journals Solvability of a Fourth-Order Boundary Value Problem with Integral Boundary Conditions

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Hui Li ◽  
Libo Wang ◽  
Minghe Pei
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Positive Solutions ◽  
Fourth Order ◽  
Order Differential Equation ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Integral Boundary Conditions ◽  
Integral Boundary ◽  
Fourth Order Differential Equation

We investigate the existence of solutions and positive solutions for a nonlinear fourth-order differential equation with integral boundary conditions of the formx(4)(t)=f(t,x(t),x′(t),x′′(t),x′′′(t)),t∈[0,1],x(0)=x′(1)=0,x′′(0)=∫01h(s,x(s),x′(s),x′′(s))ds,x′′′(1)=0, wheref∈C([0,1]×ℝ4),h∈C([0,1]×ℝ3). By using a fixed point theorem due to D. O'Regan, the existence of solutions and positive solutions for the previous boundary value problems is obtained. Meanwhile, as applications, some examples are given to illustrate our results.

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