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In this paper, we introduce three new fractional operators, MRL fractional integral, MRL fractional derivative and MC fractional derivative operators, which including generalized M-series in their kernels and give some of their fundamental properties. Then we apply Laplace, Mellin and beta integral transformations to the new fractional operators and obtain conclusions involving classical gamma and beta and modified gamma and beta functions. As examples, we also obtain similar conclusions by applying new fractional operators to the functions zλ and (1 - az)-λ. Furthermore, we present the relationships of the new fractional operators with other fractional operators in the literature. Finally, we compare the behavior of the function z² in classical Riemann-Liouville and Caputo fractional operators and MRL and MC fractional operators for orders ε = 0:2;0:4;0:6;0:8. [ABSTRACT FROM AUTHOR]

The paper is devoted to prove the existence of solutions for an infinite system of non- linear integral equations. This system is investigated in the WC-Banach algebra C(I; c0), the space of all continuous functions acting from an interval I into the sequence space c0. Making use of the measure of weak noncompactness and the weak topology, we establish some fixed point theorems for the sum and the product of nonlinear weakly sequentially continuous operat- ors acting onWC-Banach algebra involving w-contractive operators. [ABSTRACT FROM AUTHOR]

The principal aim of this paper is to serve the numerical solution for a linear integralalgebraic equation (IAE) by using Bernstein polynomials. Employing of Bernstein polynomials, the system of integral equations is approximated by the Gaussian quadrature formula with respect to the Legendre weight function. The proposed method reduces the system of integral equations to a system of algebraic equations that can be easily solved by any usual numerical method. Moreover, the convergence analysis of this algorithm will be shown by preparing some theorems. Several examples are included to illustrate the efficiency and accuracy of the proposed technique and also the results are compared with the different methods. [ABSTRACT FROM AUTHOR]

In this paper, firstly, we introduce the concept of a complex valued fuzzy b-metric space, which is inspired by the work of Shukla et al. [24]. Also, we investigate some of its topological properties which strengthen this concept. Next, we establish some fixed point theorems in the context of complex valued fuzzy b-metric spaces and give suitable examples to illustrate the usability of the obtained main results. These results extend and generalize the corresponding results given in the existing literature. Moreover, we provide some applications on the existence and uniqueness of solutions for a certain type of nonlinear integral equations. [ABSTRACT FROM AUTHOR]

In this paper, complex differential equations from first and second order with constant coefficients are solved using reduced differential transform method (RDTM). Such equations were previously solved by other methods. While obtaining a solution with these methods, the solution was reached by dividing the equation into real and imaginary parts. With the RDTM used in this study, we found that the solution can be reached without dividing the real and imaginary parts of the equation. An iteration relation is given for the solution of such equations. In addition, a variable coefficient equation was solved with RDTM. [ABSTRACT FROM AUTHOR]

In this paper, we analyze the convergence of the fitted mesh method applied to singularly perturbed Volterra delay-integro-differential equation. Our mesh comprises a special nonuniform mesh on the first subinterval and uniform mesh on another part. Error estimates are obtained using difference analogue of Gronwall's inequality with delay. A numerical test that confirms the theoretical results is presented. [ABSTRACT FROM AUTHOR]

In this paper we extend Darbo's fixed point theorem in Banach spaces and obtain a tripled fixed point theorem. The technique of measure of noncompactness is the main tool in carrying out our proof. Finally, as an application of our results, we analyze the existence of solutions for a system of neutral differential equations. [ABSTRACT FROM AUTHOR]

In this paper we will prove a fixed point theorem of Perov type for cyclic contractions on complete generalized metric spaces. Then, as an application, we will study the existence, uniqueness and approximation of the solution for a system of integral equations. [ABSTRACT FROM AUTHOR]

In this paper, we will consider the coupled fixed point problem for single-valued operators satisfying a symmetric contraction condition with respect to maximum. An application to a periodic boundary value problem illustrates the results. The study of a coupled coincidence problem is also suggested. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of generalized weakly α-contractive mappings and give some common fixed point results for this type of contraction. The presented theorems extend, generalize and improve many existing results in the literature. Two examples as well as an application to ordinary differential equations are also given in order to illustrate the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

Recently, Suzuki [T. Suzuki, A generalized Banach contraction principle that characterizes metric completeness, Proc. Amer. Math. Soc. 136 (2008), 1861-1869] proved a fixed point theorem that is a generalization of the Banach contraction principle and characterizes the metric completeness. Paesano and Vetro [D. Paesano and P. Vetro, Suzuki's type characterizations of completeness for partial metric spaces and fixed points for partially ordered metric spaces, Topology Appl., 159 (2012), 911-920] proved an analogous fixed point result for a selfmapping on a partial metric space that characterizes the partial metric 0-completeness. In this paper we prove a fixed point result for a new class of contractions of Berinde-Suzuki type on a partial metric space. Moreover, using our results, as application we obtain a new characterization of partial metric 0-completeness. Finally, we give a typical application of fixed point methods to integral equation, by using our results. [ABSTRACT FROM AUTHOR]

In this paper we investigate the boundedness of the Gerber-Shiu expected discounted penalty function applied in insurance mathematics. We give a necessary and sufficient condition for its boundedness. This condition is essentially the boundedness of the conditional expectation given the ruin occurs at the first claim. It assures that the integral equation satisfied by the Gerber- Shiu function has a unique bounded solution and it is exactly the Gerber-Shiu function. By the help of the proven necessary and sufficient condition we can also simplify the theorem concerning the necessary and sufficient condition for the limit property. We do not assume independence between the inter-claim time and the claim size but the results can be applied to the usually investigated independent case as well. We present examples to show the applicability of the condition. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence of solutions for boundary value problems of fractional differential equations of order q ∊ (0, 1] with four-point integral boundary conditions. Existence and uniqueness results are obtained by using well known fixed point theorems. Some illustrative examples are also discussed. [ABSTRACT FROM AUTHOR]

In this paper, we present a fixed point theorem for a new type of contractive mappings. Our main result extends and unifies some well-known results in the literature. [ABSTRACT FROM AUTHOR]

In this paper we present some existence, uniqueness and Hyers-Ulam stability results for the coupled fixed point of a pair of contractive type operators on complete metric spaces. The approach is based on a Perov type fixed point theorem for contractions. Some applications to integral equations and to boundary value problems are also given. [ABSTRACT FROM AUTHOR]

In this paper, we improve and further generalize some Čeby&3x0161;ev type inequalities involving functions whose derivatives belong to Lp spaces via certain integral identities. [ABSTRACT FROM AUTHOR]

In this paper, two-dimensional linear conjugate Volterra integral equations containing super-singularities in the kernels are considered. The existence of a unique solution in a certain function class is established. Formulas representing the solution are given. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the existence of a unique solution on a semi-infinite interval for quadratic integral equations with linear modification of the argument in Fréchet spaces using a nonlinear alternative of Leray-Schauder type for contraction maps in Fréchet spaces. [ABSTRACT FROM AUTHOR]