From the concept of attractor of a family of contractive affine transformations in the Euclidean plane R2, we study the fractality property of the De Rham function and other singular functions wich derive from it. In particular, we show as fractals the strong negations called k-negations.

In the first part, we investigate the singular BVP $${\frac{d}{dt}}^c{D}^{\alpha }u+{(a/t)}^c{D}^{\alpha }u=\mathscr{H}u$$ , u(0) = A, u(1) = B, c D α u(t)|t=0 = 0, where $$\mathscr{H}$$ is a continuous operator, α ∈ (0, 1) and a < 0. Here, c D denotes the Caputo fractional derivative. The existence result is proved by the Leray-Schauder nonlinear alternative. The second part establishes the relations between solutions of the sequence of problems $${\frac{d}{dt}}^c{D}^{{\alpha }_n}u+{(a/t)}^c{D}^{{\alpha }_n}u=f(t,u{,}^c{D}^{{\beta }_n}u)$$ , u(0) = A, u(1) = B, $${\left.{}^c{D}^{{\alpha }_n}u\left(t\right)\right|}_{t=0}=0$$ where a < 0, 0 < β n ≤ α n < 1, limn→∞ β n = 1, and solutions of u″+(a/t)u′ = f(t, u, u′) satisfying...

MSC 2010: 44A20, 33C60, 44A10, 26A33, 33C20, 85A99The fractional calculus of the P-transform or pathway transform which is a generalization of many well known integral transforms is studied. The Mellin and Laplace transforms of a P-transform are obtained. The composition formulae for the various fractional operators such as Saigo operator, Kober operator and Riemann-Liouville fractional integral and differential operators with P-transform are proved. Application of the P-transform in reaction rate...

Mathematics Subject Classification: 26A33, 33C20.The paper is devoted to the study of the fractional calculus of the generalized Wright function pΨq(z) defined for z ∈ C, complex ai, bj ∈ C and real αi, βj ∈ R (i = 1, 2, · · · p; j = 1, 2, · · · , q) by the series pΨq (z) It is proved that the Riemann-Liouville fractional integrals and derivative of the Wright function are also the Wright functions but of greater order. Special cases are considered.* The present investigation was partially supported...

Mathematics Subject Classification: 26A33, 31C25, 35S99, 47D07.Wentzell boundary value problem for pseudo-differential operators generating Markov processes but not satisfying the transmission condition are not well understood. Studying fractional derivatives and fractional powers of such operators gives some insights in this problem. Since an L^p – theory for such operators will provide a helpful tool we investigate the L^p –domains of certain model operators.* This work is partially supported...

MSC 2010: 26A33, 46Fxx, 58C05 Dedicated to 80-th birthday of Prof. Rudolf GorenfloWe generalize the two forms of the fractional derivatives (in Riemann-Liouville and Caputo sense) to spaces of generalized functions using appropriate techniques such as the multiplication of absolutely continuous function by the Heaviside function, and the analytical continuation. As an application, we give the two forms of the fractional derivatives of discontinuous functions in spaces of distributions.

2000 Mathematics Subject Classification: 26A33, 33C45This paper refers to a fractional order generalization of the classical Jacobi polynomials. Rodrigues’ type representation formula of fractional order is considered. By means of the Riemann–Liouville operator of fractional calculus fractional Jacobi functions are defined, some of their properties are given and compared with the corresponding properties of the classical Jacobi polynomials. These functions appear as a special case of a fractional Gauss...

We introduce function spaces $B^{p,\lambda }$ with Morrey-Campanato norms, which unify $B^{p,\lambda }$, $CM{O}^{p,\lambda }$ and Morrey-Campanato spaces, and prove the boundedness of the fractional integral operator $I_{\alpha }$ on these spaces.

Mathematics Subject Classification: 26A33, 33C60, 44A15In this paper a new special function called as M-series is introduced. This series is a particular case of the H-function of Inayat-Hussain. The M-series is interesting because the pFq -hypergeometric function and the Mittag-Leffler function follow as its particular cases, and these functions have recently found essential applications in solving problems in physics, biology, engineering and applied sciences. Let us note that the Mittag-Leffler ...

Dedicated to 75th birthday of Prof. A.M. Mathai, Mathematical Subject Classification 2010:26A33, 33C10, 33C20, 33C50, 33C60, 26A09Two integral transforms involving the Gauss-hypergeometric function in the kernels are considered. They generalize the classical Riemann-Liouville and Erdélyi-Kober fractional integral operators. Formulas for compositions of such generalized fractional integrals with the product of Bessel functions of the first kind are proved. Special cases for the product of cosine...