This paper concerns the existence of mild solutions for fractional order integro-differential equations with infinite delay. Our analysis is based on the technique of Kuratowski’s measure of noncompactness and Mönch’s fixed point theorem. An example to illustrate the applications of main results is given.
In this paper, we study the existence of integrable solutions for the set-valued differential equation of fractional type , a.e. on (0,1), , αₙ ∈ (0,1), where F(t,·) is lower semicontinuous from ℝ into ℝ and F(·,·) is measurable. The corresponding single-valued problem will be considered first.
Mathematics Subject Classification: 26A33, 34A25, 45D05, 45E10We consider ordinary fractional differential equations with Caputo-type differential operators with smooth right-hand sides. In various places in the literature one can find the statement that such equations cannot have smooth solutions. We prove that this is wrong, and we give a full characterization of the situations where smooth solutions exist. The results can be extended to a class of weakly singular Volterra integral equations.
Dedicated to Professor A.M. Mathai on the occasion of his 75-th birthday. Mathematics Subject Classi¯cation 2010: 26A33, 44A10, 33C60, 35J10.The object of this article is to present the computational solution of one-dimensional space-time fractional Schrödinger equation occurring in quantum mechanics. The method followed in deriving the solution is that of joint Laplace and Fourier transforms. The solution is derived in a closed and computational form in terms of the H-function. It provides an elegant...
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.
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.
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.