Extrait D’un Mémoire sur le développement des fonctions en séries dont les différents termes sont assujettis à satisfaire à une méme équation différentielle linéaire, contenant un paramètre variable

Abstract

L'abondance des matières nous force à différer la publication de ce Mémoire. L'extrait qu'on vient de lire a déjà été imprimé dans le Compte rendu des séances de Γ Académie des Sciences, tome IV, page 675.

Sturm–Liouville operators in the half axis with local perturbations

“…The following result is due to C. Sturm and J. Liouville [13]. For more recent references see for example [ (1) > λ (2) …”

Conformable fractional Sturm‐Liouville equation

“…Suppose that is not an eigenvalue of (29)- ( 31). Let (t, ) satisfy the equation (29) and the boundary conditions (30)- (31), where (.) ∈ L 2 (0, b).…”

“…Conversely, the function (t, ) defined by (32) satisfies (29) and ( 30)- ( 31). Green's function G (t, x, ) is unique in the sense that if there exists another functionG(t, x, ) such that (32) is satisfied, then…”

“…It is well known that the Sturm‐Liouville problems play an important role in many areas of science. It deals with the second‐order ordinary differential equation of the form The French mathematicians Sturm and Liouville were introduced first in 1837 . Since then, this field is an active field of research.…”

“…The French mathematicians Sturm and Liouville were introduced first in 1837. 29 Since then, this field is an active field of research. For a deeper discussion of the Sturm-Liouville theory, we refer the reader to the study of.…”