Abstract
In this paper, we investigate the existence and uniqueness results of intuitionistic fuzzy local and nonlocal fractional boundary value problems by employing intuitionistic fuzzy fractional calculus and some fixed-point theorems. As an application, we conclude this manuscript by giving an example to illustrate the obtained results.
Highlights
Fuzzy fractional calculus has become a powerful tool with more accurate and successful results in modeling several complex and fuzzy physical phenomena in numerous seemingly diverse and widespread fields of science and engineering
When a real physical phenomenon is modeled by a fractional initial value problem, we cannot usually be sure that the model is perfect
In order to get a perfect model under a precise initial condition, Agarwal et al, in [1], proposed the concept of fuzzy solutions for fractional differential equations with uncertainty
Summary
Fuzzy fractional calculus has become a powerful tool with more accurate and successful results in modeling several complex and fuzzy physical phenomena in numerous seemingly diverse and widespread fields of science and engineering. In order to get a perfect model under a precise initial condition, Agarwal et al, in [1], proposed the concept of fuzzy solutions for fractional differential equations with uncertainty. Arshad and Lupulescu, in [2], proved some results on the existence and uniqueness of solutions for fuzzy fractional differential equations. In [7], proved the existence and uniqueness results of solutions for initial value problem under fuzzy Caputo–Katugampola fractional derivatives. Motivated by the results mentioned above and by using the intuitionistic fuzzy sets theory introduced by Atanassov, in [14], we study the existence and uniqueness results for the following intuitionistic fuzzy local and nonlocal fractional boundary value problems: cDαX(t) F(t, X(t)), t ∈ [0, T],.
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