Volume 25, Issue 2

This paper studies neutral Liouville–Caputo-type fractional differential equations and inclusions supplemented with nonlocal Riemann–Liouville-type integral boundary conditions. Sadovskii’s fixed point theorem is applied to establish the existence result for the single-valued case, while the multivalued case is investigated by using nonlinear alternative for contractive maps. Examples are constructed to illustrate the main results. The case of nonlinear nonlocal boundary conditions is also discussed.

We introduce an infinite-order linear differential operator and study its spectrum. We show that all analytical functions around the origin are its eigenfunctions corresponding to zero eigenvalue. We outline an interesting relation between this operator and the conservation law of energy in Hamiltonian mechanics.

Let f be a non-constant meromorphic function and a=a⁢(z){a=a(z)} (≢0,∞{\not\equiv 0,\infty}) a small function of f . Here, we obtain results similar to the results due to Indrajit Lahiri and Bipul Pal [Uniqueness of meromorphic functions with their homogeneous and linear differential polynomials sharing a small function, Bull. Korean Math. Soc. 54 2017, 3, 825–838] for a more general differential polynomial by introducing the concept of weighted sharing.

In this paper, we establish the Opial-type inequalities for a conformable fractional integral and give some results in special cases of α. The results presented here would provide generalizations of those given in earlier works.

In this paper, we establish fractional Ostrowski inequalities for functions whose modulus of the first derivatives are prequasi-invex. Midpoint inequalities are also derived.

The purpose of this paper is to prove differential inequalities for meromorphic univalent functions by using a new operator associated with the Mittag-Leffler function.

Dawson’s integral and related functions in mathematical physics that include the complex error function (Faddeeva’s integral), Fried–Conte (plasma dispersion) function, Jackson function, Fresnel function and Gordeyev’s integral are analytically evaluated in terms of the confluent hypergeometric function. And hence, the asymptotic expansions of these functions on the complex plane ℂ{\mathbb{C}} are derived by using the asymptotic expansion of the confluent hypergeometric function.

Generalized Fink-type identity for multi-variables to an arbitrary time scales is obtained, giving some multi-variate Ostrowski, Iyengar and Grüss-type inequalities unifying the corresponding continuous and discrete version. Some new applications to generalized polynomials are also obtained.

In this paper, we prove a fixed point theorem for a rational type contraction mapping in the frame work of metric spaces. Also, we extend Brosowski–Meinardus type results on invariant approximation for such class of contraction mappings. The results proved extend some of the known results existing in the literature.

Kudryashov and Sinelshchikov proposed a nonlinear evolution equation that models the pressure waves in a mixture of liquid and gas bubbles by taking into account the viscosity of the liquid and the heat transfer. Conservation laws and exact solutions are computed for this underlying equation. In the analysis of this particular equation, two approaches are employed, namely, the multiplier method and Kudryashov method.