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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By applying the variational principle to a fractional action S, we obtain the fractional Euler-Lagrange equations of motion.

Inequalities for differential and integral equations. The proposed study extends the case of fuzzy differential equations of integer order. Using Wiener-Hermite expansion WHE technique in the solution of the stochastic partial differential equations SPDEs has the advantage of converting the problem to a system of deterministic equations that can be solved efficiently using the standard deterministic numerical methods [1].

The fractional derivatives are described in the sense of conformable fractional derivatives. The solutions are given in the form of series with easily computable terms. Discrete fractional calculus has also an important position in fractional calculus.

phosphate-water fractionation equation: Topics by

It is remarkable that it is established on the Cartesian product of two cones, in which the feature of two equations can be opposite. Full Text Available Priof table lookup method for solving nonlinear fractional partial differential equations fPDEs is proposed in this paper.


The series solution of this problem is obtained via the optimal homotopy analysis method OHAM. Such a system appears in quantum mechanics. The obtained results give the present method that is very effective and simple for solving the differential equations on Cantor set. We used the standard and Krasnoselskii’s fixed point theorems. We study the gronwall-bellman-ineuality between the hyperbolic and parabolic behaviors by means of the generalization of the D’Alembert formula for the classical wave equation and the invariance under space and time inversions of the interpolating fractional evolution equations Dirac like.

Fractional analysis for nonlinear electrical transmission line and nonlinear Schroedinger equations with incomplete sub- equation. This equation models the viscoelastic behavior of geological strata, metals, glasses etc.

The existence of infinitely many solutions for this equations is obtained by exploiting a recent abstract result.

Grönwall’s inequality

Reduced differential prolf method for partial differential equations within local fractional derivative operators. Existence of smooth solutions of multi-term Caputo-type fractional differential equations. The Exp-function method is extended to solve fractional partial differential equations in the sense of the modified Riemann-Liouville derivative.

The coefficients of these equations are a family of linear closed operators in the Banach space. Ciletype, some examples are given. Theorems that never existed before are introduced with their proofs. The long-term dynamic behaviors predict where systems are heading after long-term evolution.

For the second kind of equation with initial filetypf, the equivalent fractional sum form of the fractional difference equation are firstly proved. Full Text Available Similarity method is employed to solve multiterm time- fractional diffusion equation.


With the help of this concept, superconductivity could be viewed as the teleportation of electrons from one side of a superconductor to another and superfluidity could be viewed as the teleportation of helium atoms from one end of a capillary filetyp to the other. We establish the existence of a non-negative ground state solution by variational methods.

Several numerical examples are provided. The Klein—Gordon—Zakharov equations with the positive fractional. The proposed method is efficient and accurate.

differential equations – Gronwall-Bellman inequality – Mathematics Stack Exchange

Fractional differential equation with the fuzzy initial condition. On matrix fractional differential equations. A nonlocal Cauchy problem is discussed for the evolution equations. It has been shown that the fractional probability current equation is correct in the area of its applicability. Integral transform method for solving time fractional systems and fractional heat equation.

Examples illustrate the results obtained in this paper. The numerical solver was tested with the analytic solution and with Monte-Carlo simulations. We also point out how to teleport a particle to an arbitrary destination. We use mathematical induction.