Solvability of a fractional Cauchy problem based on modified fixed point results of non-compactness measures
Hemant Kumar Nashine,Rabha W. Ibrahim,Rabha W. Ibrahim,Rabha W. Ibrahim +3 more
- Vol. 4, Iss: 3, pp 847-859
TLDR
In this paper, the authors studied the solvability of a fractional Cauchy problem based on new development of fixed point theorem, where the operator is suggested to be non-compact on its domain.Abstract:
We study the solvability of a fractional Cauchy problem based on new development of fixed point theorem, where the operator is suggested to be non-compact on its domain. Moreover, we shall prove that the solution is bounded by a fractional entropy (entropy solution). For this purpose, we establish a collection of basic fixed point results, which generalizes and modifies some well known results. Our attention is toward the concept of a measure of non-compactness to generalize $\mu$-set contractive condition, using three control functions.read more
Citations
More filters
Journal ArticleDOI
The analytical analysis of nonlinear fractional-order dynamical models
TL;DR: In this paper, the analytical solution of fractional-order nonlinear Swift-Hohenberg equations using an efficient technique was proposed, which can also be used to explain the formation process in liquid surfaces bounded along a horizontally wellconducting boundary.
Journal ArticleDOI
Existence of a solution to an infinite system of weighted fractional integral equations of a function with respect to another function via a measure of noncompactness
TL;DR: In this paper , some new generalizations of Darbo's fixed-point theorem are given and the solvability of an infinite system of weighted fractional integral equations of a function with respect to another function is studied.
References
More filters
Journal ArticleDOI
Theorems about the existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem
TL;DR: In this article, the authors give three theorems about the existence and uniqueness of mild, strong, and classical solutions of a nonlocal Cauchy problem for a semilinear evolution equation.
Book
Nonlinear Integral Equations in Abstract Spaces
TL;DR: In this paper, the authors propose nonlinear Integral Equations in Banach Spaces (i.e., nonlinear integral-differential Equations) and nonlinear Impulsive Integral Eq.
Journal ArticleDOI
Fractional-order diffusion-wave equation
TL;DR: The negative-direction fractional diffusion-wave problem was studied in this article, where the existence, uniqueness, and properties of the solution of the problem were established. But the authors did not consider the non-negative-direction version of the diffusion wave problem.
Journal ArticleDOI
Generalized entropy-based criterion for consistent testing
TL;DR: In this paper, the authors generalize the Kullback and Leibler properties of entropy and propose a consistent criterion for testing relevant hypotheses such as the independence of random variables, which can be used for (physical, geophysical, economic, and biological) time series.