Geodesic
Existence and uniqueness of a mild solution for a class of the fractional evolution equation With nonlocal condition involving φ-Riemann Liouville fractional derivative
Filomat, Tome 37 (2023) no. 18, p. 6041

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DOI

In this paper, by using the fractional power of operators and theory fixed point theorems, we discuss Existence and uniqueness of mild solution to initial value problems for fractional semilinear evolution equations with compact semigroup in Banach spaces with nonlocal conditions. In particular, we derive the form of fundamental solution in terms of semigroup induced by resolvent and φ-Riemann-Liouville fractional derivatives. These results generalize previous works where the classical Riemann-Liouville fractional derivative is considered. In the end, we give an example to illustrate the applications of the abstract results.
DOI : 10.2298/FIL2318041Z
Classification : 35R11, 34K37, 26A33
Keywords: Mild solution, Fractional evolution equation, φ-Riemann-Liouville fractional derivative, convexity, Measure of noncompactness, Darbo-Sadovskii’s fixed point theorem 
Mouhssine Zakaria; Abdelaziz Moujahid; Arij Bouzelmate. Existence and uniqueness of a mild solution for a class of the fractional evolution equation With nonlocal condition involving φ-Riemann Liouville fractional derivative. Filomat, Tome 37 (2023) no. 18, p. 6041 . doi: 10.2298/FIL2318041Z
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     title = {Existence and uniqueness of a mild solution for a class of the fractional evolution equation {With} nonlocal condition involving {\ensuremath{\varphi}-Riemann} {Liouville} fractional derivative},
     journal = {Filomat},
     pages = {6041 },
     year = {2023},
     volume = {37},
     number = {18},
     doi = {10.2298/FIL2318041Z},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2318041Z/}
}
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