On the existence of solutions for fractional boundary value problems on the ethane graph
TLDR
This work investigates the existence of solutions for some fractional boundary value problems on the ethane graph and defines fractional differential equations on each edge of this graph.Abstract:
A few researchers have studied fractional differential equations on star graphs. They use star graphs because their method needs a common point which has edges with other nodes while other nodes have no edges between themselves. It is natural that we feel that this method is incomplete. Our aim is extending the method on more generalized graphs. In this work, we investigate the existence of solutions for some fractional boundary value problems on the ethane graph. In this way, we consider a graph with labeled vertices by 0 or 1, inspired by a graph representation of the chemical compound of ethane, and define fractional differential equations on each edge of this graph. Also, we provide an example to illustrate our last main result.read more
Citations
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On a new structure of the pantograph inclusion problem in the Caputo conformable setting
TL;DR: In this article, the authors reformulate and investigate the well-known pantograph differential equation by applying newly defined conformable operators in both Caputo and Riemann-Liouville settings simultaneously for the first time.
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Topological degree theory and Caputo–Hadamard fractional boundary value problems
TL;DR: In this paper, two hybrid and non-hybrid fractional boundary value problems via the Caputo-Hadamard type derivatives were studied and the existence criteria for these two problems separately.
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Two sequential fractional hybrid differential inclusions
TL;DR: In this paper, a new category of the sequential hybrid inclusion boundary value problem with three-point integro-derivative boundary conditions was introduced, and various novel analytical techniques based on α-ψ-contractive mappings, endpoints, and the fixed points of the product operators were employed to obtain the main results.
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MHD flow of generalized second grade fluid with modified Darcy’s law and exponential heating using fractional Caputo-Fabrizio derivatives
TL;DR: In this paper, the authors apply the Caputo-Fabrizio fractional derivative to the heat transformation of a second grade fluid under the effect of magneto hydrodynamic together with heat transfer as well as Darcy's law.
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A Theoretical Analysis of a Fractional Multi-Dimensional System of Boundary Value Problems on the Methylpropane Graph via Fixed Point Technique
TL;DR: In this paper , the existence and uniqueness of solutions for fractional boundary value problems on star graphs was investigated and the existence results for solutions for solutions to a new family of FFE on the methylpropane graph were proved.
References
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Book
An Introduction to the Fractional Calculus and Fractional Differential Equations
Kenneth S. Miller,Bertram Ross +1 more
TL;DR: The Riemann-Liouville Fractional Integral Integral Calculus as discussed by the authors is a fractional integral integral calculus with integral integral components, and the Weyl fractional calculus has integral components.
Book
Fractional Integrals and Derivatives: Theory and Applications
TL;DR: Fractional integrals and derivatives on an interval fractional integral integrals on the real axis and half-axis further properties of fractional integral and derivatives, and derivatives of functions of many variables applications to integral equations of the first kind with power and power-logarithmic kernels integral equations with special function kernels applications to differential equations as discussed by the authors.
Journal ArticleDOI
Positive solutions for boundary value problem of nonlinear fractional differential equation
Zhanbing Bai,Haishen Lü +1 more
TL;DR: In this paper, the positive solution of nonlinear fractional difier- ential equation with semi-positive nonlinearity was investigated and the existence results of positive solution were obtained by using Krasnosel'skii flxed point theorem.