Solutions with big graph of iterative functional equations of the second order.
Solutions with big graph of iterative functional equations of the first order
We obtain a result on the existence of a solution with big graph of functional equations of the form g(x,𝜑(x),𝜑(f(x)))=0 and we show that it is applicable to some important equations, both linear and nonlinear, including those of Abel, Böttcher and Schröder. The graph of such a solution 𝜑 has some strange properties: it is dense and connected, has full outer measure and is topologically big.
Solvability of an Infinite System of Singular Integral Equations
2000 Mathematics Subject Classification: 45G15, 26A33, 32A55, 46E15.Schauder's fixed point theorem is used to establish an existence result for an infinite system of singular integral equations in the form: (1) xi(t) = ai(t)+ ∫t0 (t − s)− α (s, x1(s), x2(s), …) ds, where i = 1,2,…, α ∈ (0,1) and t ∈ I = [0,T]. The result obtained is applied to show the solvability of an infinite system of differential equation of fractional orders.
Solvability of nonautonomous fractional integrodifferential equations with infinite delay.
Solving Fractional Diffusion-Wave Equations Using a New Iterative Method
Mathematics Subject Classification: 26A33, 31B10In the present paper a New Iterative Method [1] has been employed to find solutions of linear and non-linear fractional diffusion-wave equations. Illustrative examples are solved to demonstrate the efficiency of the method.* This work has partially been supported by the grant F. No. 31-82/2005(SR) from the University Grants Commission, N. Delhi, India.
Solving some functional and operational equations.
Some analytical properties of solutions of differential equations of noninteger order.
Some applications of differential subordination to a general class of multivalently analytic functions involving a convolution structure.
Some applications of fractional calculus in engineering.
Some applications of fractional calculus to operator semigroups and functional calculus
We survey some recent results on functional calculus for generators of holomorphic semigroups, which have been obtained using versions of fractional derivation of Riemann-Liouville or Weyl type. Such a calculus allows us to give tight estimates even in concrete L¹ examples.
Some applications of Kurzweil-Henstock integration
Applications of ideal from Kurzweil-Henstock integration to elementary analysis on , mean value theorems for vector valued functions, l’Hospital rule, theorems of Taylor type and path independence of line integrals are discussed.
Some bounding inequalities for the Jacobi and related functions.
Some characterizations of pointwise discontinuous functions
Some Characterizations of the Darboux Continuity of Real Functions
Some characterizations of the primitive of strong Henstock-Kurzweil integrable functions
In this paper we give some complete characterizations of the primitive of strongly Henstock-Kurzweil integrable functions which are defined on with values in a Banach space.
Some classes of completely monotonic functions.
Some Completely Monotonic Properties for the (p, g)-Gamma Function
MSC 2010: 33B15, 26A51, 26A48
Some considerations on the monotonicity property of power means.
Some distortion inequalities associated with the fractional derivatives of analytic and univalent functions.
Some dynamical properties of S-unimodal maps
We study 1) the slopes of central branches of iterates of S-unimodal maps, comparing them to the derivatives on the critical trajectory, 2) the hyperbolic structure of Collet-Eckmann maps estimating the exponents, and under a summability condition 3) the images of the density one under the iterates of the Perron-Frobenius operator, 4) the density of the absolutely continuous invariant measure.