Leray–Schauder Theorem for Implicit Fractional Differential Equation and Nonlocal Multi-Point Conditions

Borisut, Piyachat; Bantaojai, Thanatporn

doi:10.1007/978-981-19-0668-8_17

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2022

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“…For more applications of fractal-fractional differential equations, see [7][8][9][10] and for recent results on fractional differential equations and their applications, see [11][12][13]. To explore more results on implicit fractional differential equations and their applications, see [14][15][16][17]. There are many results relating to implicit fractional differential equations in literature involving Caputo fractional derivatives both for initial value problems (IVP) and boundary value problems (BVP) [15,[18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

On Implicit Time–Fractal–Fractional Differential Equation

Omaba

Mukiawa

Nwaeze

2022

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An implicit time–fractal–fractional differential equation involving the Atangana’s fractal–fractional derivative in the sense of Caputo with the Mittag–Leffler law type kernel is studied. Using the Banach fixed point theorem, the well-posedness of the solution is proved. We show that the solution exhibits an exponential growth bound, and, consequently, the long-time (asymptotic) property of the solution. We also give examples to illustrate our problem.

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