On Unique Solvability of a Multipoint Boundary Value Problem for Systems of Integro-Differential Equations with Involution

On boundary value problem for fractional differential equations

In this paper‎, ‎we study the existence of solutions for a‎ ‎ fractional boundary value problem‎. ‎By using critical point theory‎ ‎ and variational methods‎, ‎we give some new criteria to guarantee‎ ‎ that‎ ‎ the problems have at least one solution and infinitely many solutions.

On Unique Solvability of Boundary Value Problems for Systems of Linear Functional Differential Equations

Existence of Solutions for Fractional Integro-Differential Equation with Multipoint Boundary Value Problem in Banach Spaces

and Applied Analysis 3 where CD 0 is the Caputo’s fractional derivative, a1, a2, b1, b2, d1, and d2 are real numbers, 0 < η1, and η2 < 1. In 20 , Stanĕk has discussed the existence of positive solutions for the singular fractional boundary value problem Du t f ( t, u, u′, Du ) 0, 2 < q < 3, 0 < p < 1, u 0 0, u′ 0 u′ 1 0. 1.7 However, to the best of the author’s knowledge, a few papers can be fo...

Solvability and the Unique Solvability of a Periodic Type Boundary Value Problem for First Order Scalar Functional Differential Equations

Nonimprovable in a certain sense, sufficient conditions for the solvability and unique solvability of the problem u′(t) = F (u)(t), u(a)− λu(b) = h(u) are established, where F : C([a, b];R) → L([a, b];R) is a continuous operator satisfying the Carathéodory condition, h : C([a, b];R) → R is a continuous functional, and λ ∈ R+. 2000 Mathematics Subject Classification: 34K10.

On boundary value problems of higher order abstract fractional integro-differential equations

The aim of this paper is to establish the existence of solutions of boundary value problems of nonlinear fractional integro-differential equations involving Caputo fractional derivative by using the techniques such as fractional calculus, H"{o}lder inequality, Krasnoselskii's fixed point theorem and nonlinear alternative of Leray-Schauder type. Examples are exhibited to illustrate the main resu...