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Existence of Solution for a New Class of Fractional Differential Equations |
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PP: 361-381 |
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doi:10.18576/pfda/100303
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Author(s) |
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Hajar Sbai,
Meryeme El Harrak,
Ahmed Hajji,
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Abstract |
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| In this paper, we investigate the global existence and uniqueness of a solution to a specific class of fractional differential equations, noted by Φ-fractional differential equation with nonlocal condition, which Atangana–Baleanu Caputo fractional derivative operators and compare the two studies. At first, we need to introduce a new topology in C([0,+∞[,E) with E is a Banach space. Then, we provide the necessary hypothesis on Φ and ∥Φ∥∞ for each problem applying Banach’s fixed point theorem. Moreover, we give some illustrative examples which exhibited the applicability of the founded hypotheses.
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