in this paper we intend to offer new numerical methods to solve the second-order fuzzy abel-volterraintegro-differential equations under the generalized $h$-differentiability. the existence and uniqueness of thesolution and convergence of the proposed methods are proved in details and the efficiency of the methods is illustrated through a numerical example.

The paper presents the foundations of theory linear fractional Volterra integro-differential equations convolution type in Banach spaces. It is established that existence a resolvent operator for such equivalent to well-posedness formulation initial problem them. Within framework this approach, theorem Hille–Yosida proved.

The N -particle Schrödinger operator H(K), K ∈ (−π, π], K being the total quasi-momentum, with short-range pair potentials on lattice Z, d ≥ 1, is considered. For fixed total quasimomentum K , the structure of H(K) ’s essential spectrum is described and the analogue of the Hunziker – van Winter – Zhislin (HVZ) theorem is proved. INTRODUCTION In the sixties, fundamental results on the essential ...

The numerical contour integral method with hyperbolic contour is exploited to solve space-fractional diffusion equations. By making use of the Toeplitzlike structure of spatial discretized matrices and the relevant properties, the regions that the spectra of resulting matrices lie in are derived. The resolvent norms of the resulting matrices are also shown to be bounded outside of the regions. ...

This paper is dedicated to study a new class of general nonlinear random A-maximal m-relaxed η-accretive (so called (A, η)-accretive [49]) equations with random relaxed cocoercive mappings and random fuzzy mappings in q-uniformly smooth Banach spaces. By utilizing the resolvent operator technique for A-maximal m-relaxed η-accretive mappings due to Lan et al. and Chang’s lemma [13], some new ite...

We study static fermion bags in the 1 + 1 dimensional Gross-Neveu and NambuJona-Lasinio models. It has been known, from the work of Dashen, Hasslacher and Neveu (DHN), followed by Shei’s work, in the 1970’s, that the self-consistent static fermion bags in these models are reflectionless. The works of DHN and of Shei were based on inverse scattering theory. Several years ago, we offered an alter...

The paper deals with jump generators with a convolution kernel. Assuming that the kernel decays either exponentially or polynomially we prove a number of lower and upper bounds for the resolvent of such operators. We consider two applications of these results. First we obtain pointwise estimates for principal eigenfunction of jump generators perturbed by a compactly supported potential (so-call...

The main purpose of this paper is the existence of mild solutions for a class of first-order nonlinear delay integrodifferential equations with nonlocal initial conditions in Banach spaces. We show that the solutions are given by the application of the theory of resolvent operators and the Sadovskii’s fixed point theorem. An example is presented in the end to show the applications of the obtain...