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Using Saigo's fractional integral operators, we establish a generalized version of the Grüss type integral inequality related to the bounded integrable functions, whose bounds are integrable functions. Some special cases of our results are also considered. [ABSTRACT FROM AUTHOR]

Using Saigo's fractional integral operators, we establish a generalized version of the Grüss type integral inequality related to the bounded integrable functions, whose bounds are integrable functions. Some special cases of our results are also considered. [ABSTRACT FROM AUTHOR]

We prove the existence and uniqueness of fractional neutral impulsive differential equations with infinite delay via contraction mapping principle and fixed point technique for condensing map. We use the resolvent operator technique for integral equations to make the mild solution of the problem more appropriate. [ABSTRACT FROM AUTHOR]

This paper introduces new subclasses of analytic functions and investigate the inclusion properties of these subclasses using the generalized Bessel functions of the first kind. We also derive a variety of special cases and corollaries of the main results. [ABSTRACT FROM AUTHOR]

The current work is motivated by the so-called Caputo-type modification of the Hadamard or Caputo Hadamard fractional derivative discussed in [4]. The main aim of this paper is to study Cauchy problems for a differential equation with a left Caputo Hadamard fractional derivative in spaces of continuously differentiable functions. The equivalence of this problem to a nonlinear Volterra type integral equation of the second kind is shown. On the basis of the obtained results, the existence and uniqueness of the solution to the considered Cauchy problem is proved by using Banach's fixed point theorem. Finally, two examples are provided to explain the applications of the results. [ABSTRACT FROM AUTHOR]

The current work is motivated by the so-called Caputo-type modification of the Hadamard or Caputo Hadamard fractional derivative discussed in [4]. The main aim of this paper is to study Cauchy problems for a differential equation with a left Caputo Hadamard fractional derivative in spaces of continuously differentiable functions. The equivalence of this problem to a nonlinear Volterra type integral equation of the second kind is shown. On the basis of the obtained results, the existence and uniqueness of the solution to the considered Cauchy problem is proved by using Banach's fixed point theorem. Finally, two examples are provided to explain the applications of the results. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the existence and uniqueness of solution for fractional boundary value problem for nonlinear fractional differential equation D0α + U(t) = f(t, u(t)), 0< t < 1, 2 < α ≤ 3, with the integral boundary conditions {u(0) - γ1 u(1) = λ1 ∫0¹ g1(s, u(s))ds, u'(0) - γ2u'(1) = λ2 ∫0¹ g2(2, u(s))ds, u''(0) - γ2u''(1) = 0, where D0+α denotes Caputo derivative of order α by using the fixed point theory. We apply the contraction mapping principle and Krasnoselskii's fixed point theorem to obtain some new existence and uniqueness results. Two examples are given to illustrate the main results. [ABSTRACT FROM AUTHOR]