important generalization of the Gronwall-Bellman inequality. Proof: The assertion 1 can be proved easily. Proof It follows from [5] that T(u) satisfies (H,). Keywords: nonlinear Gronwall–Bellman inequalities; differential of the Gronwall inequality were established and then applied to prove the. At last Gronwall inequality follows from u (t) − α (t) ≤ ∫ a t β (s) u (s) d s. Btw you can find the proof in this forum at least twice share|cite|improve this.

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Zero-mass solution satisfies photon criteria and non-zero mass satisfies general theory of relativity. Variational problems with fractional derivatives: Numerical stability of the presented method with respect to all four kind of polynomials are discussed. Fractional Brownian motion and motion governed by the fractional Langevin equation in confined geometries. The Rayleigh differential equation has been generalized of fractional second order.

Examples are given to illustrate the obtained results. An example is provided to illustrate the theory. This study deals with the presence and distinction of bounded m-solutions type mild for a family of generalized integral and differential equations of spot order with fractional resolvent and indefinite delay. The obtained results are compared with the results obtained via other techniques.

differential equations – Gronwall-Bellman inequality – Mathematics Stack Exchange

Discrete fractional calculus has also an important position in fractional calculus. Motivated by grondall-bellman-inequality motion of gronwwall-bellman-inequality observed in living cells, we study the stochastic properties of a non-Brownian particle whose motion is governed by either fractional Brownian motion or the fractional Langevin equation and restricted to a finite domain.

Thus we prove some inequalities for conformable integrals by using the generalization of Sturm’s separation and Sturm’s comparison theorems. As for applications, oscillation for two certain fractional differential equations with damping term is investigated by the use of the presented results. In this paper, we present a new stable numerical approach based on the operational matrix of integration of Jacobi polynomials for solving fractional delay differential equations FDDEs.

In order to have a better representation of these physical models, fractional calculus is used. Bifurcation dynamics of the tempered fractional Langevin equation. Home Questions Tags Users Unanswered. We prove the Hermiticity of the fractional Hamilton operator and establish the parity conservation law for fractional quantum mechanics.


The obtained solutions include generalized trigonometric and hyperbolic function gronwall-bellman-iequality. The suggested technique is easily applicable and effectual which can be implemented successfully to obtain the solutions for different types of nonlinear FPDEs.

By the quotient rule. The method yields a powerful numerical algorithm for fractional order derivative to implement. Fractional hydrodynamic equations for fractal media.

The book covers fundamental concepts of multivalued analysis and introduces a new class of mixed initial value problems involving the Hadamard derivative and Riemann-Liouville fractional integrals. Many problems of filtration of liquids in gronwall-bellman-ineuqality high porous medium lead to the need to study boundary value problems for partial differential equations in fractional order.

Grönwall’s inequality

The coefficients of these equations are a family of linear closed operators in the Banach space. The obtained results are given to present the accuracy of the technology to solve the steady heat-conduction in fractal media.

The fundamental solution of these problems is established and its moments are calculated. Moreover, the exact solutions are gronwall-bellan-inequality for the equations which are formed by different parameter values related to the time- fractional -generalized fifth-order KdV equation. Also numerical examples are carried out for various types of problems, including the Bagley-Torvik, Ricatti and composite fractional oscillation equations for the application of the method.

Grönwall’s inequality – Wikipedia

hronwall-bellman-inequality Full Text Available In this paper, we investigate the local fractional Laplace equation in the steady heat-conduction problem. This methodical technique is based on the representation of the neutron density as a power series of the relaxation time as a small parameter. The approach is a generalization to our recent work for single fractional differential equations.

As a result, some new exact solutions for them are successfully established.

Using Gronwall-bellman-ineuqality fixed point theorem, the existence and uniqueness of solutions is studied for this kind of fractional differential equations. We derive the gronwall-bellman-ineequality equation for fractal media. The operators are taken in the local fractional sense. On matrix fractional differential equations. In addition, some very useful corollaries are established and their proofs presented in detail.

Flietype solutions of fractional differential equations with derivative terms. In order to core calculation in the nuclear reactors there is a new version of neutron diffusion equation which is established on the fractional partial derivatives, named Neutron Fractional Diffusion Equation NFDE. A basic matrix equation which corresponds to a system of fractional equations is utilized, and a new system of nonlinear algebraic equations is obtained.


Numerical results, figures, and comparisons have been presented to confirm the theoretical results and efficiency of the proposed method. Denoising is one of the most fundamental image restoration problems in computer vision and image processing. Full Text Available Similarity method is employed to solve multiterm time- fractional diffusion equation.

We formulate a general fractional LBE approach and exemplify it with a particularly simple case of the Bohm and Gross scattering integral filletype to a fractional generalization of the Bhatnagar, Gross and Krook BGK kinetic equation.

Robust fast controller design via nonlinear fractional differential equations. The fractional integrals and derivatives of fractional integro-differential equations are widely used in modern investigations of theoretical physics, mechanics, and applied mathematics.

Differential transform method; fractional Fisher equation. Through a comprehensive study based in part on their recent research, the authors address the issues gronwalll-bellman-inequality to initial and boundary value problems involving Hadamard type differential equations and inclusions as well oroof their functional counterparts.

In this study, we implement a well known transformation technique, Differential Transform Method DTMto the area of fractional differential equations.

Our approach is show-cased by solving the fractional Fisher and fractional Allen-Cahn reaction-diffusion equations in two and three spatial dimensions, and analyzing the speed gronwall-bellman-iequality the traveling wave and size of the interface in terms of the fractional power of the underlying Laplacian operator.

By an appropriate choice of the dispersive exponent, both mass. Existence of a coupled system of fractional differential equations.

Full Text Available The modified Kudryashov method is powerful, efficient and can be used as an alternative to establish new solutions of different type of fractional differential equations applied in mathematical physics.