Volterra equations with fractional stochastic integrals

El-Borai, Mahmoud M.; El-Nadi, Khairia El-Said; Mostafa, Osama L.; Ahmed, Hamdy M.

doi:10.1155/s1024123x04312020

Cited by 22 publications

(10 citation statements)

References 11 publications

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“…Now we will apply the described method above to Eqs. (28). To begin with, we suppose (29) Where, , , and , are arbitrary constants to be determined later.…”

Section: Example 41 Consider Thenonlinearcomplexfractional Schrödingmentioning

confidence: 99%

Exact Solutions Of Some Nonlinear complex fractional Partial Differential Equations

El-Borai¹,

Al-Masroub²

2016

IJMTT

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In this paper, we used the sub-equation method for solving the nonlinear complex fractional Schrödinger equation, the nonlinear complex fractional Kundu-Eckhaus, and nonlinear complex fractional generalized-Zakharov equations in the sense oftheJumarie's modified Riemann-Liouvillederivative. Whit the aid of the mathematical software Maple, some exact solutions for these equations are successfully. KEYWORDS: Sub-equation method, exact solutions ofsomenonlinearcomplex fractionalpartial differential equations.

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“…Now we will apply the described method above to Eqs. (28). To begin with, we suppose (29) Where, , , and , are arbitrary constants to be determined later.…”

Section: Example 41 Consider Thenonlinearcomplexfractional Schrödingmentioning

confidence: 99%

Exact Solutions Of Some Nonlinear complex fractional Partial Differential Equations

El-Borai¹,

Al-Masroub²

2016

IJMTT

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“…The equation (2.12) is called fractional differential equations that governs the stock model (Black-Scholes), ([3], [8], [18], [20], [22]).…”

Section: Generalized Fractional Hybrid Equationsmentioning

confidence: 99%

“…It is used for studying simple dynamical systems, but it also describes complex physical systems. For example, applications of the fractional calculus can be found in chaotic dynamics, control theory, stochastic modeling, but also in finance, hydrology, biophysics, physics, astrophysics, cosmology and so on ( [5], [6], [8], [9], [10]). But some other fields have just started to study problems from fractional point of view.…”

Section: Introductionmentioning

confidence: 99%

Generalized Fractional Hybrid Hamilton–pontryagin Equations

Chiş

Opris

2011

Int. J. Geom. Methods Mod. Phys.

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In this paper we present a new approach on the study of dynamical systems. Combining the two ways of expressing the uncertainty, using probabilistic theory and credibility theory, we have investigated the generalized fractional hybrid equations. We have introduced the concepts of generalized fractional Wiener process, generalized fractional Liu process and the combination between them, generalized fractional hybrid process. Corresponding generalized fractional stochastic, respectively fuzzy, respectively hybrid dynamical systems were defined. We have applied the theory for generalized fractional hybrid Hamilton–Pontryagin (HP) equation and generalized fractional Hamiltonian equations. We have found fractional Langevin equations from the general fractional hybrid Hamiltonian equations. For these cases and specific parameters, numerical simulations were done.

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“…The qualitative properties of stochastic fractional differential equations have been considered only in few publications. El-Borai et al [16] studied the existence uniqueness, and continuity of the solution of a fractional stochastic integral equation. Ahmed [17] derived a set of sufficient conditions for controllability of fractional stochastic delay equations by using a stochastic version of the well-known Banach fixed point theorem and semigroup theory.…”

Section: Introductionmentioning

confidence: 99%

Asymptotic Stability of Fractional Stochastic Neutral Differential Equations with Infinite Delays

Sakthivel

Revathi

Mahmudov

2013

Abstract and Applied Analysis

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We study the existence and asymptotic stability inpth moment of a mild solution to a class of nonlinear fractional neutral stochastic differential equations with infinite delays in Hilbert spaces. A set of novel sufficient conditions are derived with the help of semigroup theory and fixed point technique for achieving the required result. The uniqueness of the solution of the considered problem is also studied under suitable conditions. Finally, an example is given to illustrate the obtained theory.

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Volterra equations with fractional stochastic integrals

Abstract: Some fractional stochastic systems of integral equations are studied. The fractional stochastic Skorohod integrals are also studied. The existence and uniquness of the considered stochastic fractional systems are established. An application of the fractional Black-Scholes is considered.

Cited by 22 publications

References 11 publications

Exact Solutions Of Some Nonlinear complex fractional Partial Differential Equations

Exact Solutions Of Some Nonlinear complex fractional Partial Differential Equations

Generalized Fractional Hybrid Hamilton–pontryagin Equations

Asymptotic Stability of Fractional Stochastic Neutral Differential Equations with Infinite Delays

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