Abstract
A coupled system of singular fractional differential equations involving Riemann–Liouville integral and Caputo derivative is considered in this paper. The question of existence and uniqueness of solutions is studied using Banach contraction principle. Furthermore, the question of existence of at least one solution is discussed. At the end, an illustrative example is given in details.
Highlights
Fractional calculus theory and differential equations of non integer order are new powerful mathematical tools for modeling complex real world phenomena, see for instance the papers [1,2,3]for more details
The study of coupled systems of fractional order is important in various problems of applied sciences, see for instance the two research works [12,16,17,18,19]
We prove the following first main result: Theorem 1
Summary
Fractional calculus theory and differential equations of non integer order are new powerful mathematical tools for modeling complex real world phenomena, see for instance the papers [1,2,3]for more details. Fractional calculus theory and differential equations of non integer order are new powerful mathematical tools for modeling complex real world phenomena, see for instance the papers [1,2,3]. For more information and more details and recent applications, we refer the reader to [4,5,6,7,8,9]. We refer the reader to the papers [10,11,12,13,14,15]. The study of coupled systems of fractional order is important in various problems of applied sciences, see for instance the two research works [12,16,17,18,19]
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