Quadratic integral equations of fractional order have been studied from different views. Here we shall study the existence continuous solutions a ϕ− fractional-orders quadratic functional equation, establish some properties these and prove maximal minimal that equation. Moreover, introduce particular cases to illustrate our results.

Laplace transform and some of the author’s previous results about first order differential-recurrence equations with discrete auto-convolution are used to solve a new type of non-linear quadratic integral equation. This paper continues the author’s work from other articles in which are considered and solved new types of algebraic-differential or integral equations.

The continuous-time random walk (CTRW) is a pure-jump stochastic process with several applications not only in physics but also in insurance, finance, and economics. A definition is given for a class of stochastic integrals driven by a CTRW, which includes the Itō and Stratonovich cases. An uncoupled CTRW with zero-mean jumps is a martingale. It is proved that, as a consequence of the martingal...

We present a computational approach for finding all integral solutions of the equation y2 = 1k + 2k + · · ·+xk for even values of k. By reducing this problem to that of finding integral solutions of a certain class of quartic equations closely related to the Pell equations, we are able to apply the powerful computational machinery related to quadratic number fields. Using our approach, we deter...

In this paper, a numerical method is proposed for solving optimal control problem of Volterra integral equations using radial basis functions (RBFs) for approximating unknown function. Actually, the method is based on interpolation by radial basis functions including multiquadrics (MQs), to determine the control vector and the corresponding state vector in linear dynamic system while minimizing...

We consider a very general quadratic integral equation and we prove the existence of monotonic solutions of this equation in C[0,1]. Our analysis depends on a suitable combination of the measure of noncompactness introduced by Banaś and Olszowy and the Darabo fixed point theorem.

Abstract We investigate the existence of solutions for a nonlinear integral inclusion Urysohn–Stieltjes type. As applications, we give Chandrasekhar quadratic equation and inclusion.

We study the solvability of a quadratic integral equation of fractional order with linear modification of the argument. This equation is considered in the Banach space of real functions defined, bounded and continuous on an unbounded interval. Moreover, we will obtain some asymptotic characterization of solutions. AMS Mathematics Subject Classification : 45G10, 45M99, 47H09.

The theory of differential and integral equations of fractional order has recently received a lot of attention and now constitutes a significant branch of nonlinear analysis. Numerous research papers and monographs have appeared devoted to differential and integral equations of fractional order cf., e.g., 1–6 . These papers contain various types of existence results for equations of fractional ...