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This paper considers a new fuzzy fractional differential variational inequality with integral boundary conditions comprising a fuzzy fractional differential inclusion with integral boundary conditions and a variational inequality in…

The essentials of fractional calculus according to different approaches that can be useful for our applications in the theory of probability and stochastic processes are established. In addition to this, from this fractional integral one…

In this paper, we introduce a new method for calculating fractional integrals and differentials. The method involves an equation that we have obtained from infinite applied integration by parts. The equation works for special class of…

The close form of some integrals involving recently developed generalized k-Struve functions is obtained. The outcome of these integrations is expressed in terms of generalized Wright functions. Several special cases are deduced which lead…

We review the recent generalized fractional calculus of variations. We consider variational problems containing generalized fractional integrals and derivatives and study them using indirect methods. In particular, we provide necessary…

The umbral restyling of hypergeometric functions is shown to be a useful and efficient approach in simplifying the associated computational technicalities. In this article, the authors provide a general introduction to the umbral version of…

In this PhD thesis we introduce a generalized fractional calculus of variations. We consider variational problems containing generalized fractional integrals and derivatives, and study them using standard (indirect) and direct methods. In…

The ostrowski inequality expresses bounds on the deviation of a function from its integral mean. The aim of this paper is to establish a new inequality using weight function which generalizes the inequalities of Dragomir, Wang and Cerone…

Our main purpose is to establish Gagliardo-Nirenberg type inequalities using fractional homogeneous Sobolev spaces, and homogeneous Besov spaces. In particular, we extend some of the results obtained by the authors in [1, 2, 3, 7, 16, 21].

Simple inequalities are established for some integrals involving the modified Bessel functions of the first and second kind. In most cases, we show that we obtain the best possible constant or that our bounds are tight in certain limits. We…

In this paper, we consider a linear fractional differential equation with fractional boundary conditions. First, by obtaining Green's function, we derive the Lyapunov-type inequalities for such boundary value problems. Furthermore, we use…

In this paper, we provide some new generalizations of Feng Qi type integral inequalities on time scales by using elementary analytic methods.

In this paper, through the introduction of partial multiple weights, we firstly study the related Rubio de Francia extrapolation theorem within the framework of partial Muckenhoupt classes and further obtain the corresponding extrapolation…

In this paper, we investigate the solutions for a generalized fractional diffusion equation that extends some known diffusion equations by taking a spatial time-dependent diffusion coefficient and an external force into account, which…

We provide a general framework for fractional Hardy inequalities. Our framework covers, for instance, fractional inequalities related to the Dirichlet forms of some L\'evy processes, and weighted fractional inequalities on irregular open…

We generalize the well-known mean value inequality of subharmonic functions for a slightly more general function class. We also apply this generalized mean value inequality to weighted boundary behavior and nonintegrability questions of…

This paper is devoted to study the nonlinear sequential fractional boundary value problems involving generalized $\psi$-Caputo fractional derivatives with nonlocal boundary conditions. We investigate the Green function and some of its…

In this paper we first extend a generalization of Ostrowski type inequality on time scales for functions whose derivatives are bounded and then unify corresponding continuous and discrete versions. We also point out some particular integral…

We establish some nonlinear integral inequalities for functions defined on a time scale. The results extend some previous Gronwall and Bihari type inequalities on time scales. Some examples of time scales for which our results can be…

In this paper, a general integral identity for a twice differentiable functions is derived. By using of this identity, the author establishes some new Hermite-Hadamard type and Simpson type inequalities for differentiable…