A Class of Nonlinear Boundary Value Problems for an Arbitrary Fractional-Order Differential Equation with the Riemann-Stieltjes Functional Integral and Infinite-Point Boundary Conditions
Date
2018
Authors
Srivastava, H.M.
El-Sayed, Ahmed M. A.
Gaafar, Fatma M.
Journal Title
Journal ISSN
Volume Title
Publisher
Symmetry
Abstract
In this paper, we investigate the existence of an absolute continuous solution to a class
of first-order nonlinear differential equation with integral boundary conditions (BCs) or with
infinite-point BCs. The Liouville-Caputo fractional derivative is involved in the nonlinear function.
We first consider the existence of a solution for the first-order nonlinear differential equation with
m-point nonlocal BCs. The existence of solutions of our problems is investigated by applying the
properties of the Riemann sum for continuous functions. Several examples are given in order to
illustrate our results.
Description
Keywords
nonlinear boundary value problems, fractional-order differential equations, Riemann-Stieltjes functional integral, Liouville-Caputo fractional derivative, infinite-point boundary conditions, advanced and deviated arguments, existence of at least one solution
Citation
Srivastava, H. M., El-Sayed, A. M. A., & Gaafar, F. M. (2018). A Class of Nonlinear Boundary Value Problems for an Arbitrary Fractional-Order Differential Equation with the Riemann- Stieltjes Functional Integral and Infinite-Point Boundary Conditions. Symmetry. 10(10), 1- 13. https://doi.org/10.3390/sym10100508.