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
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 cons...
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| Format: | Article |
| Language: | English |
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MDPI AG
2018-10-01
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| Series: | Symmetry |
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| Online Access: | http://www.mdpi.com/2073-8994/10/10/508 |
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| author | Hari M. Srivastava Ahmed M. A. El-Sayed Fatma M. Gaafar |
| author_facet | Hari M. Srivastava Ahmed M. A. El-Sayed Fatma M. Gaafar |
| author_sort | Hari M. Srivastava |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-13T00:27:19Z |
| format | Article |
| id | doaj.art-e511fe5b591d4931bd8947cc62d58625 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-04-13T00:27:19Z |
| publishDate | 2018-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-e511fe5b591d4931bd8947cc62d586252022-12-22T03:10:35ZengMDPI AGSymmetry2073-89942018-10-01101050810.3390/sym10100508sym10100508A Class of Nonlinear Boundary Value Problems for an Arbitrary Fractional-Order Differential Equation with the Riemann-Stieltjes Functional Integral and Infinite-Point Boundary ConditionsHari M. Srivastava0Ahmed M. A. El-Sayed1Fatma M. Gaafar2Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, CanadaDepartment of Mathematics, Faculty of Science, Alexandria University, Alexandria 21500, EgyptDepartment of Mathematics, Faculty of Science, Damanhour University, Damanhour 22516, EgyptIn 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.http://www.mdpi.com/2073-8994/10/10/508nonlinear boundary value problemsfractional-order differential equationsRiemann-Stieltjes functional integralLiouville-Caputo fractional derivativeinfinite-point boundary conditionsadvanced and deviated argumentsexistence of at least one solution |
| spellingShingle | Hari M. Srivastava Ahmed M. A. El-Sayed Fatma M. Gaafar 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 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 |
| title | 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 |
| title_full | 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 |
| title_fullStr | 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 |
| title_full_unstemmed | 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 |
| title_short | 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 |
| title_sort | class of nonlinear boundary value problems for an arbitrary fractional order differential equation with the riemann stieltjes functional integral and infinite point boundary conditions |
| topic | 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 |
| url | http://www.mdpi.com/2073-8994/10/10/508 |
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