Eulerian numbers with fractional order parameters.
P.L. Butzer, M. Hauss (1993)
Aequationes mathematicae
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P.L. Butzer, M. Hauss (1993)
Aequationes mathematicae
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PHIL DIAMOND (1971)
Aequationes mathematicae
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A. Sklar (1969)
Aequationes mathematicae
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Marek Cezary Zdun (1985)
Aequationes mathematicae
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B. Martić (1964)
Matematički Vesnik
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Masayoshi Hata (2005)
Acta Arithmetica
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Helena Musielak (1973)
Colloquium Mathematicae
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Branislav Martić (1973)
Publications de l'Institut Mathématique
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Gülçin Bozkurt, Durmuş Albayrak, Neşe Dernek (2019)
Applications of Mathematics
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We use the Laplace transform method to solve certain families of fractional order differential equations. Fractional derivatives that appear in these equations are defined in the sense of Caputo fractional derivative or the Riemann-Liouville fractional derivative. We first state and prove our main results regarding the solutions of some families of fractional order differential equations, and then give examples to illustrate these results. In particular, we give the exact solutions for...
Sandeep P. Bhairat, Dnyanoba-Bhaurao Dhaigude (2019)
Mathematica Bohemica
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This paper is devoted to studying the existence of solutions of a nonlocal initial value problem involving generalized Katugampola fractional derivative. By using fixed point theorems, the results are obtained in weighted space of continuous functions. Illustrative examples are also given.
Yuji Liu, Pinghua Yang (2014)
Applicationes Mathematicae
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The purpose of this paper is to study global existence and uniqueness of solutions of initial value problems for nonlinear fractional differential equations. By constructing a special Banach space and employing fixed-point theorems, some sufficient conditions are obtained for the global existence and uniqueness of solutions of this kind of equations involving Caputo fractional derivatives and multiple base points. We apply the results to solve the forced logistic model with multi-term...
Astha Chauhan, Rajan Arora (2019)
Communications in Mathematics
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In this work, the fractional Lie symmetry method is applied for symmetry analysis of time fractional Kupershmidt equation. Using the Lie symmetry method, the symmetry generators for time fractional Kupershmidt equation are obtained with Riemann-Liouville fractional derivative. With the help of symmetry generators, the fractional partial differential equation is reduced into the fractional ordinary differential equation using Erdélyi-Kober fractional differential operator. The conservation...