Stability of solutions for generalized fractional differential problems by applying significant inequality estimates release_2cbefokgmnhw5cgkulhuft4yiq

by Mohammed D. Kassim, Thabet Abdeljawad, Saeed M. Ali, Mohammed S. Abdo

Published in Advances in Difference Equations by Springer Science and Business Media LLC.

2021   Volume 2021

Abstract

<jats:title>Abstract</jats:title>In this research paper, we intend to study the stability of solutions of some nonlinear initial value fractional differential problems. These equations are studied within the generalized fractional derivative of various orders. In order to study the solutions' decay to zero as a power function, we establish sufficient conditions on the nonlinear terms. To this end, some versions of inequalities are combined and generalized via the so-called Bihari inequality. Moreover, we employ some properties of the generalized fractional derivative and appropriate regularization techniques. Finally, the paper involves examples to affirm the validity of the results.
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