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In this paper, we examine the existence and uniqueness of solutions under the traveling wave forms for a free boundary Cauchy problem of space-fractional Jordan-Moore-Gibson-Thompson equations of nonlinear acoustics, which describe sound propagation in thermo-viscous elastic terms. It does so by applying the properties of Schauder's and Banach's fixed point theorems, while Caputo's fractional derivative is used as the differential operator. For application purposes, some examples of explicit solutions are provided to demonstrate the usefulness of our main results. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and analyze various classes of vector-valued (Dasymptotically) ρ-almost periodic type distributions in Rn. We also provide certain applications of our theoretical results to the (abstract) partial differential equations. [ABSTRACT FROM AUTHOR]

In this paper we establish for a bounded linear operator defined on a Banach space several sufficient and necessary conditions for which property (gaw) holds. In this work, we consider commutative perturbations by algebraic operator and quasinilpotent operator for T ϵ B(X ) such that T* satisfies property (gaw). We prove that if A is an algebraic and T ϵ PS(X ) is such that AT = TA, then f(T* + A*) satisfies property (gaw) for every f ϵ Hc(σ(T + A)). Moreover, we show that if Q is a quasi-nilpotent operator and T ϵ PS(X ) is such that TQ = QT, then f(T* + Q*) satisfies the property (gaw) for every f ϵ Hc((T + Q)). At the end of this paper, we apply the obtained results to a number of subclasses of PS(X ). [ABSTRACT FROM AUTHOR]

In this paper, we consider an iterative procedure for approximating common fixed points of two generalized asymptotically quasi-nonexpansive mappings and we prove some strong and weak convergence theorems for such mappings in uniformly convex Banach spaces.This will extend the results of Cholamjiak and Suantai, Khan and those generalized therein to the case of generalized asymptotically quasi-nonexpansive mappings and by a faster iterative procedure. [ABSTRACT FROM AUTHOR]

In this manuscript we have generalized the result of B. R. Reddy and C. J. S. Reddy [8]. We have taken R to be a prime ring with nonzero ideal I of R and G be a symmetric generalized biderivation of R.We have investigated the commutativity of R if G satisfies any one of the given identities (i) G([l,m], n)±[l,m] = 0, (ii) G(l◦m, n)±l◦m = 0, (iii) G(l,m) ◦ G(m, n) = 0, (iv) [G(l,m),G(m, n)] = 0, (v) G(l,m) ◦ G(m, n) ± l ◦ n = 0 and (vi) [G(l,m),G(m, n)] ± [l, n] = 0 ∀ l, m, n ∈ I. [ABSTRACT FROM AUTHOR]

We employ the fact that L1 (G) is n-weakly amenable for each n ≥ 1 to show that for an inverse semigroup S with the set of idempotents E, l1(S) is n-weakly module amenable as an L1(E)-module with trivial left action. We study module amenability and weak module amenability of the module projective tensor products of Banach algebras. [ABSTRACT FROM AUTHOR]