Generalized Taylor's formula

By Zaid M. Odibat, Nabil T. Shawagfeh. Applied Mathematics and Computation, 2007

1,003 citations recorded by the source corpus.

Subfields: Applied Mathematics, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/5bf222e6216cb479c39a79bf2115ab8b36fd3de4

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In Applied Mathematics

In Modeling and Simulation

In Numerical Analysis

Citations in the corpus

A Caputo fractional derivative of a function with respect to another function (2016, methodology): “Using the semigroup law for integrals and Theorem 4, we get For a similar result involving the Caputo fractional derivative, that is, when ψ ( x ) = x , we mention [22].”
A new approach to the Pontryagin maximum principle for nonlinear fractional optimal control problems (2015, neutral): “ere b(t) is a bounded and monotonic increasing function on [0,T), then u(t) ≤ a(t) + Zt 0 " X∞ n=1 (b(t)Γ(α))n Γ(nα) (t −s)nα−1a(s) # ds, t ∈ [0,T) Theorem 2.4. Generalized Taylor’s formula (cf. [15, 16]). Let 0 < α ≤ 1 , n ∈ N, f(·) be a continuous function in [a,b], CDkα a f(·) ∈ C[a,b] ∀k”
A Fractional Order SEIR Model with Density Dependent Death Rate ABSTRACT | FULL TEXT (2011, background): “For the proof of the theorem about non-negative solutions we shall need the following Lemma [14]: 3.”
Mathematical modeling of time fractional reaction-diffusion systems (2008, neutral): “In this case, the solution of the vector equation (7) is given by Mittag–Leffler functions [28,26,24,35]”
On tempered fractional calculus with respect to functions and the associated fractional differential equations (2021, background): “The proofs are following the lines of [42, 43].”
A numerical study of fractional relaxation–oscillation equations involving $$\psi $$ψ-Caputo fractional derivative (2018, methodology): “This method is based on a fractional version of Taylor’s formula established in [21].”
Fractional conservation of mass (2008, methodology): “A recent breakthrough in fractional calculus has given us a tool that is extremely useful in solving this problem: the fractional Taylor series [14].”