Displaying similar documents to “Fractional distance domination in graphs”

Theorems on some families of fractional differential equations and their applications

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...

On contraction principle applied to nonlinear fractional differential equations with derivatives of order α ∈ (0,1)

Małgorzata Klimek (2011)

Banach Center Publications

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One-term and multi-term fractional differential equations with a basic derivative of order α ∈ (0,1) are solved. The existence and uniqueness of the solution is proved by using the fixed point theorem and the equivalent norms designed for a given value of parameters and function space. The explicit form of the solution obeying the set of initial conditions is given.

A detailed analysis for the fundamental solution of fractional vibration equation

Li-Li Liu, Jun-Sheng Duan (2015)

Open Mathematics

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In this paper, we investigate the solution of the fractional vibration equation, where the damping term is characterized by means of the Caputo fractional derivative with the order α satisfying 0 < α < 1 or 1 < α < 2. Detailed analysis for the fundamental solution y(t) is carried out through the Laplace transform and its complex inversion integral formula. We conclude that y(t) is ultimately positive, and ultimately decreases monotonically and approaches zero for the case...

Positive solutions for Hadamard differential systems with fractional integral conditions on an unbounded domain

Tariboon Jessada, Sotiris K. Ntouyas, Suphawat Asawasamrit, Chanon Promsakon (2017)

Open Mathematics

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In this paper, we investigate the existence of positive solutions for Hadamard type fractional differential system with coupled nonlocal fractional integral boundary conditions on an infinite domain. Our analysis relies on Guo-Krasnoselskii’s and Leggett-Williams fixed point theorems. The obtained results are well illustrated with the aid of examples.

The general solution of impulsive systems with Riemann-Liouville fractional derivatives

Xianmin Zhang, Wenbin Ding, Hui Peng, Zuohua Liu, Tong Shu (2016)

Open Mathematics

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In this paper, we study a kind of fractional differential system with impulsive effect and find the formula of general solution for the impulsive fractional-order system by analysis of the limit case (as impulse tends to zero). The obtained result shows that the deviation caused by impulses for fractional-order system is undetermined. An example is also provided to illustrate the result.

Fractional-order Bessel functions with various applications

Haniye Dehestani, Yadollah Ordokhani, Mohsen Razzaghi (2019)

Applications of Mathematics

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We introduce fractional-order Bessel functions (FBFs) to obtain an approximate solution for various kinds of differential equations. Our main aim is to consider the new functions based on Bessel polynomials to the fractional calculus. To calculate derivatives and integrals, we use Caputo fractional derivatives and Riemann-Liouville fractional integral definitions. Then, operational matrices of fractional-order derivatives and integration for FBFs are derived. Also, we discuss an error...

Time fractional Kupershmidt equation: symmetry analysis and explicit series solution with convergence analysis

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...

A Neighborhood Condition for Fractional ID-[A, B]-Factor-Critical Graphs

Sizhong Zhou, Fan Yang, Zhiren Sun (2016)

Discussiones Mathematicae Graph Theory

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Let G be a graph of order n, and let a and b be two integers with 1 ≤ a ≤ b. Let h : E(G) → [0, 1] be a function. If a ≤ ∑e∋x h(e) ≤ b holds for any x ∈ V (G), then we call G[Fh] a fractional [a, b]-factor of G with indicator function h, where Fh = {e ∈ E(G) : h(e) > 0}. A graph G is fractional independent-set-deletable [a, b]-factor-critical (in short, fractional ID-[a, b]- factor-critical) if G − I has a fractional [a, b]-factor for every independent set I of G. In this paper, it...