A Cauchy problem for some fractional differential equation via deformable derivatives
M. Mebrat
Department of Mathematics, Morgan State University, 1700 E. Cold Spring Lane, Baltimore, M.D. 21251, USA
G. M. N'Guérékata
Department of Mathematics, Morgan State University, 1700 E. Cold Spring Lane, Baltimore, M.D. 21251, USA
Received on September 14, 2019
Accepted on January 9, 2020
Communicated by Maximilian F. Hasler
| Abstract. Abstract. In this paper we investigate further properties of the new concept of deformable derivative and use the results to study the existence (and uniqueness) of mild solutions to the Cauchy problem for the nonlinear differential equation with nonlocal conditions Dαx(t) = f(t, x(t)), t ∈ [0, T ], x(0) + g(x) = x0, where Dαx(t) is the deformable derivative of x, 0 < α < 1. We use the Krasnoselkii’s theorem to achieve our main result. | |
| Keywords: | Deformable derivative, Krasnoselskii’s theorem, mild solution. |
| 2010 Mathematics Subject Classification: 34G20, 34A08. | |