Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Note on the Conformable Boundary Value Problems: Sturm’s Theorems and Green’s Function

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. Preprints 2020, 2020090440 (doi: 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 (doi: 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.

Subject Areas

Conformable fractional derivative; Conformable fractional integral; Conformable fractional differential equations; Sturm´s Theorems; Green´s Function

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