Hilfer-Hadamard Nonlocal Integro-Multipoint Fractional Boundary Value Problems

Solvability of Nonlocal Fractional Boundary Value Problems

Nonlocal Boundary Value Problems for Hybrid Fractional Differential Equations and Inclusions of Hadamard Type

This paper investigates the existence of solutions for nonlocal boundary value problems of nonlinear hybrid fractional differential equations and inclusions of Hadamard type. We make use of fixed point theorems due to Dhage [7], [8] to obtain the existence results. We also discuss some examples for illustration of the main results.

Nonlocal Boundary Value Problems

The theory of the nonlocal linear boundary value problems is still on the level of examples. Any attempt to encompass them by a unified scheme sticks upon the lack of general methods. Here we are to outline an algebraic approach to linear nonlocal boundary value problems. It is based on the notion of convolution of linear operator and on operational calculus on it. Our operators are right inver...

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...

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...