Abstract
This research paper is dedicated to an investigation of an evolution problem under a new operator (g-Atangana–Baleanu–Caputo type fractional derivative)(for short, g-ABC). For the proposed problem, we construct sufficient conditions for some properties of the solution like existence, uniqueness and stability analysis. Existence and uniqueness results are proved based on some fixed point theorems such that Banach and Krasnoselskii. Furthermore, through mathematical analysis techniques, we analyze different types of stability results. The symmetric properties aid in identifying the best strategy for getting the correct solution of fractional differential equations. An illustrative example is discussed for the control problem.
Highlights
Arbitrary integration and differentiation are some of the most interesting research fields because they are suitable tools for modeling complex phenomena in a wide range of science and engineering fields, such as chemical engineering, electrodynamics, power systems, biological sciences, etc
Motivated by the above argumentations, we investigate the sufficient conditions for the existence and uniqueness as well as different types of stability results for an important class of differential equations, called evolution equations which used to explain the law of differentiation to describe the development of dynamic systems described as follows
Fractional derivative with a nonsingular kernel has attracted a lot of attention in the recent past due to some physical phenomena that are difficult to model as a result of the singularities
Summary
Department of Statistics and Informatics Techniques, Technical College of Management-Mosul, Northern Department of Mathematics, Faculty of Science, Hadhramout University, Mukalla 50512, Yemen Department of Automation, Biomechanics and Mechatronics, Lodz University of Technology, 1/15 Stefanowski St., 90-924 Lodz, Poland These authors contributed equally to this work.
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