‎The present paper is devoted to the existence and uniqueness result of the fractional evolution equation $D^{q}_c u(t)=g(t,u(t))=Au(t)+f(t)$‎ ‎for the real $qin (0,1)$ with the initial value $u(0)=u_{0}intilde{R}$‎, ‎where $tilde{R}$ is the set of all generalized real numbers and $A$ is an operator defined from $mathcal G$ into itself‎. Here the Caputo fractional derivative $D^{q}_c$ is used i...

and Applied Analysis 3 Subject to the initial condition D α−k 0 U (x, 0) = f k (x) , (k = 0, . . . , n − 1) , D α−n 0 U (x, 0) = 0, n = [α] , D k 0 U (x, 0) = g k (x) , (k = 0, . . . , n − 1) , D n 0 U (x, 0) = 0, n = [α] , (11) where ∂α/∂tα denotes the Caputo or Riemann-Liouville fraction derivative operator, f is a known function, N is the general nonlinear fractional differential operator, a...

In this paper, we study sufficient conditions for existence and uniqueness of solutions of three point boundary vale problem for p-Laplacian fractional order differential equations. We use Schauder's fixed point theorem for existence of solutions and concavity of the operator for uniqueness of solution. We include some examples to show the applicability of our results.

This paper introduces an image denoising algorithm based on generalized Srivastava-Owa fractional differential operator for removing Gaussian noise in digital images. The structures of n n× fractional masks are constructed by this algorithm. Experiments show that, the capability of the denoising algorithm by fractional differential-based approach appears efficient to smooth the Gaussian noisy i...

let $t$ be a bounded operator on the banach space $x$ and $ph$ be an analytic self-map of the unit disk $bbb{d}$‎. ‎we investigate some operator theoretic properties of‎ ‎bilateral composition operator $c_{ph‎, ‎t}‎: ‎f ri t circ f circ ph$ on the vector-valued hardy space $h^p(x)$ for $1 leq p leq‎ ‎+infty$.‎ ‎compactness and weak compactness of $c_{ph‎, ‎t}$ on $h^p(x)$‎ ‎are characterized an...

The present work focuses on entropy solutions for the fractional Cauchy problem of nonsymmetric systems. We impose sufficient conditions on the parameters to obtain bounded solutions of L∞. The solutions attained are unique and exclusive. Performance is established by utilizing the maximum principle for certain generalized time and space-fractional diffusion equations. The fractional differenti...

The main objective of this paper is to introduce k-fractional derivative operator by using the definition of k-beta function. We establish some results related to the newly defined fractional operator such as Mellin transform and relations to khypergeometric and k-Appell’s functions. Also, we investigate the k-fractional derivative of k-Mittag-Leffler and Wright hypergeometric functions.