In this article, we establish certain sufficient conditions to show the existence of solutions a fractional differential equation with ?-Riemann-Liouville and ?-Caputo derivative in special Banach space. Our approach is based on fixed point theorems for Meir-Keeler condensing operators via measure non-compactness. Also an example given illustrate our approach.

In the finance market, it is well known that price change of underlying fractal transmission system can be modeled with Black-Scholes equation. This article deals finding approximate analytic solutions for time-fractional equation fractional integral boundary condition a European option pricing problem in Katugampola derivative sense. It generalizes both Riemann–Liouville and Hadamard derivativ...

A bstract I consider Pauli-Villars’ regulators for the ghosts in path-integral string formulation and show how they preserve conformal invariance. calculate regulator contributions to effective action central charge demonstrate consistency of mean-field quantization Nambu-Goto 2 < d 26. The higher-derivative corrections Liouville are briefly considered Pauli-Villars proper-time regularizatio...

In this article, we introduce the fractional differential systems in the sense of the Weber fractional derivatives and study the asymptotic stability of these systems. We present the stability regions and then compare the stability regions of fractional differential systems with the Riemann-Liouville and Weber fractional derivatives.

This paper builds on the notion of the so-called orthogonal derivative, where an n-th order derivative is approximated by an integral involving an orthogonal polynomial of degree n. This notion was reviewed in great detail in a paper by the author and Koornwinder in 2012. Here, an approximation of the Weyl or Riemann–Liouville fractional derivative is considered by replacing the n-th derivative...

In this article, we study some class of fractional boundary value problem involving generalized Riemann Liouville derivative with respect to a function and the p-Laplace operator. Precisely, using variational methods combined mountain pass theorem, prove that such has nontrivial weak solution. Our main result significantly complement improves previous papers in literature.

Abstract The article contains the comparative use analysis of fractional derivative three types (Riemann -Liouville, Caputo and model) at Begley -Torvik equation when modeling deformation strength characteristics polymer concrete. We also consider how to obtain a solution initial value problem for model using recurrent kernels sequence. Further, correctness is substantiated establishing type or...

The paper consider an inhomogeneous creep equation arising from a generalized Voigt model containing Riemann-Liouville fractional derivative of the order 0 < β 1. Laplace transform is used for numerical solution. obtained solutions are compared with experimental data polymer concrete samples. On basis this comparison conclusion about adequacy solution method made, and estimates parameters gi...

using the riemann-liouville fractional differintegral operator, the lie theory is reformulated. the fractional poisson bracket over the fractional phase space as 3n state vector is defined to be the fractional lie derivative. its properties are outlined and proved. a theorem for the canonicity of the transformation using the exponential operator is proved. the conservation of its generator is p...

Abstract We study distributed optimal control problems, governed by space-time fractional parabolic equations (STFPEs) involving time-fractional Caputo derivatives and spatial of Sturm-Liouville type. first prove existence uniqueness solutions STFPEs on an open bounded interval their regularity. Then we show to a quadratic problem. derive adjoint problem using the right-Caputo derivative in tim...