Boundary value problem for abstract first order differential equation with integral condition

Numerical solution for boundary value problem of fractional order with approximate Integral and derivative

Approximating the solution of differential equations of fractional order is necessary because fractional differential equations have extensively been used in physics, chemistry as well as engineering fields. In this paper with central difference approximation and Newton Cots integration formula, we have found approximate solution for a class of boundary value problems of fractional order. Three...

Nonlocal Boundary Value Problem for Second Order Abstract Elliptic Differential Equation

We establish conditions that guarantee Fredholm solvability in the Banach space Lp of nonlocal boundary value problems for elliptic abstract differential equations of the second order in an interval. Moreover, in the space L2 we prove in addition the coercive solvability, and the completeness of root functions (eigenfunctions and associated functions). The obtained results are then applied to t...

Positive solutions for higher - order nonlinear fractional differential equation with integral boundary condition ∗

In this paper, we study a kind of higher-order nonlinear fractional differential equation with integral boundary condition. The fractional differential operator here is the Caputo’s fractional derivative. By means of fixed point theorems, the existence and multiplicity results of positive solutions are obtained. Furthermore, some examples given here illustrate that the results are almost sharp.

Periodic Boundary Value Problem for First Order Impulsive Differential Equation at Resonance

We develop a general theorem concerning the existence of solutions to the periodic boundary value problem for the first-order impulsive differential equation,    x′(t) = f(t, x(t)), t ∈ J \ {t1, t2, · · · , tk} 4x(ti) = Ii(x(ti)), i = 1, 2 · · · k x(0) = x(T ). And using it we get a concrete existence result. Moreover, to our knowledge the coincidence degree method has not been used to t...

Second-Order Boundary Value Problem with Integral Boundary Conditions