Abstract
In this paper, we discuss the solvability of a class of multiterm initial value problems involving the Caputo–Fabrizio fractional derivative via the Laplace transform. We derive necessary and sufficient conditions to guarantee the existence of solutions to the problem. We also obtain the solutions in closed forms. We present two examples to illustrate the validity of the obtained results.
Highlights
There is great interest to develop new types of fractional derivatives of nonsingular kernel
Stability analysis of fractional differential equations without inputs was studied in [7], where exponential stability is obtained for the Caputo–Fabrizio derivative
We apply the Laplace transform to analyze the solutions of the fractional initial value problems (3) and (4). is paper is organized as follows: in Section 2, we present some preliminary results about the Caputo–Fabrizio fractional derivative and derive necessary and sufficient conditions to guarantee the existence of solutions to problems (3) and (4)
Summary
There is great interest to develop new types of fractional derivatives of nonsingular kernel. Stability analysis of fractional differential equations without inputs was studied in [7], where exponential stability is obtained for the Caputo–Fabrizio derivative. Since their kernels are nonlocal, fractional derivatives preserve memories, and they have been used to model several (SIR) epidemic models (see [8,9,10,11,12,13,14]). We apply the Laplace transform to analyze the solutions of the fractional initial value problems (3) and (4). Is paper is organized as follows: in Section 2, we present some preliminary results about the Caputo–Fabrizio fractional derivative and derive necessary and sufficient conditions to guarantee the existence of solutions to problems (3) and (4).
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