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
Abstract
:1. Introduction
2. Preliminaries
3. Existence of Solutions to (1) with the -Point BCs (4)
- (i)
- The function is a Carathéodory function, that is, it possesses the following properties:
- (a)
- For each is continuous;
- (b)
- For each is measurable.
- (ii)
- The function is continuous and advanced, or continuous and deviated, .
- (iii)
- There exists an integrable function and a constant such that
4. Riemann-Stieltjes Functional Integral BCs
5. Infinite-Point Boundary Conditions
6. Further Illustrative Examples
7. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Srivastava, H.M.; El-Sayed, A.M.A.; Gaafar, F.M. 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 2018, 10, 508. https://doi.org/10.3390/sym10100508
Srivastava HM, El-Sayed AMA, Gaafar FM. 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. 2018; 10(10):508. https://doi.org/10.3390/sym10100508
Chicago/Turabian StyleSrivastava, Hari M., Ahmed M. A. El-Sayed, and Fatma M. Gaafar. 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, no. 10: 508. https://doi.org/10.3390/sym10100508