FINITE FRACTIONAL-ORDER OF DISTRIBUTIONAL SOLUTIONS OF CERTAIN FRACTIONAL DIFFERENTIAL EQUATIONS

K. Boonpoonmee; Somsak Orankitjaroen; P. Pasom; K. Nonlaopon

K. Boonpoonmee
Somsak Orankitjaroen
P. Pasom
K. Nonlaopon

Keywords: Fractional diﬀerential equations, Dirac delta function, generalized functions, Riemann-Liouville fractional derivative

Abstract

We establish necessary and suﬃcient conditions for the existence of solutions of certain fractional diﬀerential equations in the form of ﬁnite fractional-order of Dirac delta functions. We then give some fractional diﬀerential equations whose solutions are in such a form.