Green’s functional for a higher order ordinary integro-differential equation with nonlocal conditions

2016 ◽  
Author(s):  
Kemal Özen
Keyword(s):  
Differential Equation ◽  
Nonlocal Conditions ◽  
Higher Order ◽  
Integro Differential Equation

scholarly journals ASYMPTOTIC EXPANSION OF SOLUTION OF GENERAL BVP WITH INITIAL JUMPS FOR HIGHER-ORDER SINGULARLY PERTURBED INTEGRO-DIFFERENTIAL EQUATION

2018 ◽  
pp. 28-36
Author(s):  
Dauylbayev M. ◽  
Atakhan N. ◽  
Mirzakulova A.E.
Keyword(s):  
Differential Equation ◽  
Asymptotic Expansion ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Higher Order ◽  
Singularly Perturbed ◽  
Jump Phenomenon ◽  
Integro Differential Equation ◽  
Asymptotic Expansion Of Solution ◽  
Initial Jump

In this article we constructed an asymptotic expansion of the solution undivided boundary value problem for singularly perturbed integro-differential equations with an initial jump phenomenon m – th order. We obtain the theorem about estimation of the remainder term’s asymptotic with any degree of accuracy in the smallparameter.

scholarly journals Controllability Analysis for Impulsive Integro-differential Equation via AB Fractional Derivative

2021 ◽  
Author(s):  
KALIMUTHU KALIRAJ ◽  
E. Thilakraj ◽  
Ravichandran C ◽  
Kottakkaran Nisar
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Fractional Derivative ◽  
Fractional Order ◽  
Point Theorem ◽  
Nonlocal Conditions ◽  
Banach Fixed Point Theorem ◽  
Integro Differential Equation

In this work, we analyse the controllability for certain classes of impulsive integro - differential equations(IIDE) of fractional order via Atangana Baleanu derivative involving finite delay with initial and nonlocal conditions using Banach fixed point theorem.

Initial problem for a nonlinear integro-differential equation with a higher-order hyperbolic operator and with reflection of the argument

2020 ◽  
pp. 31-56
Author(s):  
T.K. Yuldashev ◽  
J.A. Artykova
Keyword(s):  
Differential Equation ◽  
Initial Value Problem ◽  
Higher Order ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Degenerate Kernel ◽  
Hyperbolic Operator ◽  
Initial Value ◽  
Partial Differential ◽  
Integro Differential Equation

In this paper it is studied the questions of one value solvability of initial value problem for nonlinear integro-differential equation with hyperbolic operator of the higher order, with degenerate kernel and reflective argument for regular values of spectral parameter. It is expressed the partial differential operator on the left-hand side of equation of higher order by the superposition of first-order partial differential operators. This is allowed us to present the considering integro-differential equation as an integral equation, describing the change of the unknown function along the characteristic. Further is applied the method of degenerate kernel. In proof of the theorem on one-value solvability of initial value problem is applied the method of successive approximations. Also is proved the stability of this solution with respect to the initial functions.

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