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This manuscript is mainly focusing on the approximate controllability and the null controllability for fractional neutral stochastic partial differential equations with delay driven by Rosenblatt p...

In this paper, we introduce the mild solution for a new class of noninstantaneous and nonlocal impulsive Hilfer fractional stochastic integrodifferential equations with fractional Brownian motion and Poisson jumps. The existence of the mild solution is derived for the considered system by using fractional calculus, stochastic analysis and Sadovskii’s fixed point theorem. Finally, an example is also given to show the applicability of our obtained theory.

In this paper, the exp-function method is applied to construct exact solutions and soliton solutions of (n+1)-dimensional modified Zakharov–Kuznetsov (mZK) equation. Solitary and topological soliton solutions are obtained. These solutions are significant importance for studying waves in plasma physics.

By using fractional calculus, stochastic analysis theory and fixed point theorems, sufficient conditions for approximate controllability of nonlocal Sobolev-type neutral fractional stochastic diffe...

In this paper, by using the extended simplest equation method, we study the Manakov system. Beside bright, dark and singular solitons, periodic solutions, hyperbolic functions solutions and rational functions are obtained. Moreover, the graphs for some solutions are presented.

In this paper, we investigate the sufficient conditions for null controllability of noninstantaneous impulsive Hilfer fractional stochastic integrodifferential system with the Rosenblatt process and Poisson jump. The required results are obtained based on fractional calculus, stochastic analysis, and Sadovskii’s fixed point theorem. Finally, an example is given to illustrate the obtained results.

By using fractional calculus and fixed point theorems, existence of mild solution for nonlinear Hilfer fractional integro-partial differential system is studied. In addition, sufficient conditions for controllability of Hilfer fractional integro-partial differential system is established.

By using stochastic analysis, fractional analysis, compact semigroups and the Schauder fixed-point theorem, we discuss the approximate boundary controllability of a nonlocal Hilfer fractional stochastic differential system with fractional Brownian motion and a Poisson jump. In addition, we establish the sufficient conditions for exact null controllability for the same problem. Finally, an example is given to illustrate the results obtained.

In this paper, COVID-19 dynamics are modelled with three mathematical dynamic models, fractional order modified SEIRF model, stochastic modified SEIRF model, and fractional stochastic modified SEIRF model, to characterize and predict virus behavior. By using Euler method and Euler-Murayama method, the numerical solutions for the considered models are obtained. The considered models are applied to the case study of Egypt to forecast COVID-19 behavior for the second virus wave which is assumed to be started on 15 November 2020. Finally, comparisons between actual and predicted daily infections are presented.

In this article, periodic averaging method for impulsive conformable fractional stochastic differential equations with Poisson jumps are discussed. By using stochastic analysis, fractional calculus, Doob's martingale inequality and Cauchy-Schwarz inequality, we show that the solution of the conformable fractional impulsive stochastic differential equations with Poisson jumps converges to the corresponding averaged conformable fractional stochastic differential equations with Poisson jumps and without impulses.

In this paper, we study the existence and uniqueness of mild solutions for neutral delay Hilfer fractional integrodifferential equations with fractional Brownian motion. Sufficient conditions for controllability of neutral delay Hilfer fractional differential equations with fractional Brownian motion are established. The required results are obtained based on the fixed point theorem combined with the semigroup theory, fractional calculus and stochastic analysis. Finally, an example is given to illustrate the obtained results.

In this paper, we investigate the existence of mild solutions of Hilfer fractional stochastic integro-differential equations with nonlocal conditions. The main results are obtained by using fractional calculus, semigroups and Sadovskii fixed point theorem. In the end, an example is given to illustrate the obtained results.

In this work, we consider a class of conformable fractional stochastic differential equations driven by Rosenblatt process. By employing stochastic analysis, fractional calculus and fixed point theorem, we investigate the approximate controllability and null controllability results for the considered problems. Finally, two examples are introduced to explain the obtained results.

The solitons in birefringent optical fibers with Hamiltonian perturbations and Kerr law nonlinearity is studied in this paper. By using the modified extended direct algebraic method, we obtained soliton solutions and other solutions for complex Ginzburg-Landau (CGL) equation having kerr law nonlinearity with Hamiltonian terms. Bright solitons, dark solitons, singular solitons, Weierstrass elliptic, plane wave, hyperbolic, exponential, singular periodic and periodic wave solutions are reported. Finally, for the physical illustration of the obtained solutions, 3D and 2D graphs are presented.

Sobolev-type nonlocal fractional differential systems with Clarke’s subdifferential are studied. Sufficient conditions for controllability and constrained controllability for Sobolev-type nonlocal fractional differential systems with Clarke’s subdifferential are established, where the time fractional derivative is the Hilfer derivative. An example is given to illustrate the obtained results.

This paper is concerned with Hilfer fractional stochastic delay differential equations with Poisson jumps. Under some assumptions, we obtain an averaging principle for the solution of the considered system. The required results are obtained based on fractional calculus, Doob’s martingale inequality and Cauchy–Schwarz inequality.

A nonlinear transmission line (NLTL) is comprised of a transmission line periodically loaded with varactors, where the capacitance nonlinearity arises from the variable depletion layer width, which depends both on the DC and AC voltages of the propagating wave. An equivalent circuit model of NLTL is discussed analytically, in this article, and different type of solutions are celebrated. The improved extended tanh-function method has been applied successfully to extract the solutions. The obtained solutions are solitary wave solutions, singular periodic solutions, singular soliton solutions, Jacobi elliptic doubly periodic type solutions and Weierstrass elliptic doubly periodic type solutions. It is a very convenient tool to study the propagation of electrical solitons which propagate in the form of voltage waves in nonlinear dispersive media.

Existence and controllability results for nonlinear Hilfer fractional differential equations are studied. Sufficient conditions for existence and approximate controllability for Sobolev-type impulsive fractional differential equations are established, where the time fractional derivative is the Hilfer derivative. An example for Sobolev-type Hilfer fractional delay partial differential equation with impulsive condition is considered.

In this paper, we prove the existence of mild solutions for a class of semilinear neutral fractional stochastic integro-differential equations with nonlocal conditions. Sufficient conditions for the existence are derived with the help of the Sadovskii fixed point theorem. In the end, an example is given to show the application of our results.

In this paper we study the numerical solutions of the stochastic differential equations of the formdu(x,t)=f(x,t,u)dt+g(x,t,u)dW(t)+@?|q|= R^n^x^n,andA"q:R^@nx[0,T]->R^n^x^n,where (A"q,|q|=

Haussmann in [Journal of mathematical analysis and applications (1978)] discussed asymptotic stability in infinite dimension of the stochastic differential equationdX+AXdt=BXdWwhere A is a closed linear operator generating strongly continuous semigroup, B is a bounded operator, W is a Wiener process on a separable Hilbert space with covariance operator Z. Also Curtain [J. Math. Anal. Appl. (1981)] and others [Proceedings of the First Arabic Conference in Physics and Mathematics, Baghdad, 1978; Annals Prob. 24 (2) (1996); J. Math. Anal. Appl. (1978)] discussed the stability of a similar equations contains first and a second order derivatives. In this work we study the stability and solution of equation of the formdX+(A+Q)Xdt=BXdWwhere Q is a general closed linear operator.

Approximate controllability for impulsive neutral stochastic functionaldifferential equations with finite delay and fractional Brownian motion in aHilbert space are studied. The results are obtained by using semigroup theory,stochastic analysis, and Banach’s fixed point theorem. Finally, an exampleis given to illustrate the application of our result. MSC: 60H15, 60G22, 93B05, 34A37.

In the present paper, we deal with the fractional neutral differential equations involving nonlocal initial conditions. The existence of mild solutions are established. The results are obtained by using the fractional power of operators and the Sadovskii’s fixed point theorem. An application to a fractional partial differential equation with nonlocal initial condition is also considered.

In this paper, by using compact semigroups and the Schauder fixed-point theorem, we study the sufficient conditions for controllability of Sobolev type fractional integro-differential systems in a Banach space. An example is provided to illustrate the obtained results.

Sufficient conditions for boundary controllability of nonlinear fractional integrodifferential systems in Banach space are established. The results are obtained by using fixed point theorems. We also give an application for integropartial differential equations of fractional order.