Version 1
: Received: 17 September 2020 / Approved: 18 September 2020 / Online: 18 September 2020 (12:16:52 CEST)
How to cite:
Martínez, F.; Martínez, I.; Kaabar, M. K. A.; Paredes, S. Note on the Conformable Boundary Value Problems: Sturm’s Theorems and Green’s Function. Preprints2020, 2020090440. https://doi.org/10.20944/preprints202009.0440.v1
Martínez, F.; Martínez, I.; Kaabar, M. K. A.; Paredes, S. Note on the Conformable Boundary Value Problems: Sturm’s Theorems and Green’s Function. Preprints 2020, 2020090440. https://doi.org/10.20944/preprints202009.0440.v1
Martínez, F.; Martínez, I.; Kaabar, M. K. A.; Paredes, S. Note on the Conformable Boundary Value Problems: Sturm’s Theorems and Green’s Function. Preprints2020, 2020090440. https://doi.org/10.20944/preprints202009.0440.v1
APA Style
Martínez, F., Martínez, I., Kaabar, M. K. A., & Paredes, S. (2020). Note on the Conformable Boundary Value Problems: Sturm’s Theorems and Green’s Function. Preprints. https://doi.org/10.20944/preprints202009.0440.v1
Chicago/Turabian Style
Martínez, F., Mohammed K. A. Kaabar and Silvestre Paredes. 2020 "Note on the Conformable Boundary Value Problems: Sturm’s Theorems and Green’s Function" Preprints. https://doi.org/10.20944/preprints202009.0440.v1
Abstract
Recently, the conformable derivative and its properties have been introduced. In this paper, we propose and prove some new results on conformable Boundary Value Problems. First, we introduce a conformable version of classical Sturm´s separation, and comparison theorems. For a conformable Sturm-Liouville problem, Green's function is constructed, and its properties are also studied. In addition, we propose the applicability of the Green´s Function in solving conformable inhomogeneous linear differential equations with homogeneous boundary conditions, whose associated homogeneous boundary value problem has only trivial solution. Finally, we prove the generalized Hyers-Ulam stability of the conformable inhomogeneous boundary value problem.
Computer Science and Mathematics, Applied Mathematics
Copyright:
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