In this paper, Bernoulli wavelets are presented for solving (approximately) fractional differential equations in a large interval. Bernoulli wavelets operational matrix of fractional order integration is derived and utilized to reduce the fractional differential equations to system of algebraic equations. Numerical examples are carried out for various types of problems, including fractional Van...

In this article‎, ‎the multi-step conformable fractional differential transform method (MSCDTM) is applied to give approximate solutions of the conformable fractional-order differential systems‎. ‎Moreover‎, ‎we check the stability of conformable fractional-order L"{u} system with the MSCDTM to demonstrate the efficiency and effectiveness of the proposed procedure.

In this paper, applying two theorems of Ricceri and Bonanno, we will establish the existence of three weak solutions for a quasilinear elliptic system. Indeed, we will assign a differentiable nonlinear operator to a differential equation system such that the critical points of this operator are weak solutions of the system. In this paper, applying two theorems of R...

this paper is devoted to the study of establishing sufficient conditions forexistence and uniqueness of positive solution to a class ofnon-linear problems of fractional differential equations. the boundary conditionsinvolved riemann-liouville fractional order derivative and integral. further, the non-linear function $f$ containfractional order derivative which produce extra complexity. thank to...

the present study introduces a new technique of homotopy perturbation method for the solution of systems of fractional partial differential equations. the proposed scheme is based on laplace transform and new homotopy perturbation methods. the fractional derivatives are considered in caputo sense. to illustrate the ability and reliability of the method some examples are provided. the results ob...

We discuss the continuity of analytic resolvent in the uniform operator topology and then obtain the compactness of Cauchy operator by means of the analytic resolvent method. Based on this result, we derive the existence of mild solutions for nonlocal fractional differential equations when the nonlocal item is assumed to be Lipschitz continuous and neither Lipschitz nor compact, respectively. A...

the purpose of this paper is to study the fuzzy fractional differentialequations. we prove that fuzzy fractional differential equation isequivalent to the fuzzy integral equation and then using this equivalenceexistence and uniqueness result is establish. fuzzy derivative is considerin the goetschel-voxman sense and fractional derivative is consider in theriemann liouville sense. at the end, we...

The stable difference scheme for the approximate solution of the initial value problem du(t) dt + D 1 2 t u(t) + Au(t) = f(t), 0 < t < 1, u(0) = 0 for the differential equation in a Banach space E with the strongly positive operator A and fractional operator D 1 2 t is presented. The well-posedness of the difference scheme in difference analogues of spaces of smooth functions is established. In...

In this paper, by introducing the concept of a generalized concave operator and the properties of cone and monotone iterative technique in ordered Banach spaces, some new existence and uniqueness theorems of fixed points for the operator under more extensive conditions are obtained. Finally, as applications, we apply the results obtained in this paper to study the existence and uniqueness of po...

We study the existence of mild solutions for a class of impulsive fractional partial neutral stochastic integro-differential inclusions with statedependent delay. We assume that the undelayed part generates a solution operator and transform it into an integral equation. Sufficient conditions for the existence of solutions are derived by using the nonlinear alternative of Leray-Schauder type for...