A Multidimensional Fixed‐Point Theorem and Applications to Riemann‐Liouville Fractional Differential Equations

Nabil, Tamer; Soliman, Ahmed H.

doi:10.1155/2019/3280163

Cited by 4 publications

(4 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Tamer Nabil et al, [40] werecompared with other available solutions from existing methods by using graphicalrepresentations and numerical computations. The results reveal that the proposedmethod was most suitable in terms of computational cost efficiency, and accuracywhich can be applied to find solutions of nonlinear fractional reactiondiffusionequations.…”

Section: Review Related On Fixed Point Theorem Applicationsmentioning

confidence: 99%

Existence of solutions for fixed point theorem

.Malathi¹,

Chelliah²

2021

JUSST

View full text Add to dashboard Cite

The development of a mathematical model based on diffusion has received a great dealof attention in recent years, many scientist and mathematician have tried to apply basicknowledge about the differential equation and the boundary condition to explain anapproximate the diffusion and reaction model. The subject of fractional calculus attracted much attentions and is rapidly growing area of research because of itsnumerous applications in engineering and scientific disciplines such as signal processing, nonlinear control theory, viscoelasticity, optimization theory [1], controlled thermonuclear fusion, chemistry, nonlinear biological systems, mechanics,electric networks, fluid dynamics, diffusion, oscillation, relaxation, turbulence, stochastic dynamical system, plasmaphysics, polymer physics, chemical physics, astrophysics, and economics. Therefore, it deserves an independent theoryparallel to the theory of ordinary differential equations (DEs).In the development of non-linear analysis, fixed point theory plays an important role. Also, it has been widely used in different branches of engineering and sciences. Banach fixed point theory is a essential part of mathematical analysis because of its applications in various area such as variational and linear inequalities, improvement and approximation theory. The fixed-point theorem in diffusion equations plays a significant role to construct methods to solve the problems in sciences and mathematics. Although Banach fixed point theory is a vast field of study and is capable of solving diffusion equations. The main motive of the research is solving the diffusion equations by Banach fixed point theorems and Adomian decomposition method. To analysis the drawbacks of the other fixed-point theorems and different solving methods, the related works are reviewed in this paper.

show abstract

Section: Review Related On Fixed Point Theorem Applicationsmentioning

confidence: 99%

Existence of solutions for fixed point theorem

.Malathi¹,

Chelliah²

2021

JUSST

View full text Add to dashboard Cite

show abstract

“…Furthermore, the deterministic conformable PDEs turned into a significant subject in mathematical physics. At this regard, the KdV and stochastic KdV equations have been solved by many ideas related to the conformable derivative [8,[12][13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

“…Applying the degree balance between the linear and nonlinear terms of maximum order in equation ( 16), we can specify the values of λ and h. Using direct calculation, we have l h = . In a similar way, we balance the linear and nonlinear terms of minimum order in equation (16) and specify the values of μ and q. Also, we can get m q = .…”

mentioning

confidence: 99%

Closed-form solutions of stochastic KdV equation with generalized conformable derivatives

Soliman

Hyder

2020

Phys. Scr.

View full text Add to dashboard Cite

With the assistance of Hermite transform, we use the Exp-function technique to solve the Wick-type stochastic KdV equation with a generalized type of conformable derivatives. The exact solutions of the stochastic KdV equation are obtained in a white noise environment. Two new kinds of Brownian motion functional solutions, including soliton and periodic solutions are presented. The graphs for a portion of these exact solutions have been given by picking peculiar values of the existing parameters to visualize the proposed technique of the given KdV equation.

show abstract

“…The fixed point theorems are powerful technique to obtain the existence of solution of these problem. There are many of fixed point theorems can be applied to obtain the solution of mathematical models [24,25]. Krasnoselskii's and Banach fixed point theorems play an important role to obtain the existence of solution of a lot of mathematical problems [35].…”

Section: Introductionmentioning

confidence: 99%

A Multidimensional Fixed‐Point Theorem and Applications to Riemann‐Liouville Fractional Differential Equations

Cited by 4 publications

References 20 publications

Existence of solutions for fixed point theorem

Existence of solutions for fixed point theorem

Closed-form solutions of stochastic KdV equation with generalized conformable derivatives

On Nonlinear Fractional Neutral Differential Equation with the ψ-Caputo Fractional Derivative

Contact Info

Product

Resources

About