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Fractional differential equations with a Caputo derivative with respect to a Kernel function and their applications
Author(s) -
Almeida Ricardo,
Malinowska Agnieszka B.,
Monteiro M.Teresa T.
Publication year - 2017
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4617
Subject(s) - mathematics , uniqueness , fractional calculus , nonlinear system , differential equation , kernel (algebra) , mathematical analysis , derivative (finance) , initial value problem , pure mathematics , physics , quantum mechanics , financial economics , economics
This paper is devoted to the study of the initial value problem of nonlinear fractional differential equations involving a Caputo‐type fractional derivative with respect to another function. Existence and uniqueness results for the problem are established by means of the some standard fixed point theorems. Next, we develop the Picard iteration method for solving numerically the problem and obtain results on the long‐term behavior of solutions. Finally, we analyze a population growth model and a gross domestic product model with governing equations being fractional differential equations that we have introduced in this work.