On Some Existence and Uniqueness Results for a Class of Equations of Order0<α≤1on Arbitrary Time Scales

Abstract

This paper investigates the existence and uniqueness of solution for a class of nonlinear fractional differential equations of fractional order0&lt;α≤1in arbitrary time scales. The results are established using extensions of Krasnoselskii-Krein, Rogers, and Kooi conditions.

Cauchy’s formula on nonempty closed sets and a new notion of Riemann–Liouville fractional integral on time scales

“…A different approach is proposed in [9], where the fractional integral on time scales is introduced by integrating on the time scale but making use of the classical Euler's gamma function Γ. Although such notion is now being used, with success, in several contexts and by different authors, see, e.g., [5,15,20,22,23], here we show that the definition of [9] is not the most natural one on time scales.…”

A Qualitative Study on Fractional Logistic Integro-differential Equations in an Arbitrary Time Scale

“…See, for example [13,16,17,27,28,[33][34][35]38] and references cited therein. Over the past few years different researchers have qualitatively studied fractional integro-differential equations and time scales integro-differential equations separately, see [1,4,5,11,12,21,32] and references cited therein. But as per our knowledge, a less number of work has been reported in the combined treatment for time scale fractional integro-differential equations.…”