In this article, we develop the distributed order fractional hybrid differential equations (DOFHDEs) with linear perturbations involving the fractional Riemann-Liouville derivative of order $0 < q < 1$ with respect to a nonnegative density function. Furthermore, an existence theorem for the fractional hybrid differential equations of distributed order is proved under the mixed $varphi$-Lipschit...

in this article, we study the analytical solutions of different parabolic heat equations with different boundaryconditions in the form of multi-term fractional differential equations. then we compare these analytical solutions with numerical finite difference methods. this comparison demonstrates the accuracy of the analytical and numerical methods presented here.

We establish interior and up to the boundary Hölder regularity estimates for weak solutions of Dirichlet problem fractional g−Laplacian with bounded right hand side g convex. These are first results available in literature integro-differential equations context Orlicz–Sobolev spaces.

In this paper, we analyze various classes of multi-dimensional Stepanov $\rho$-almost periodic functions in general metric. The main structural properties for the introduced almost type are established. We also provide an illustrative application to abstract degenerate semilinear fractional differential equations.

In this paper, we investigate the oscillation of a class generalized proportional fractional integro-differential equations with forcing term. We present sufficient conditions to prove some criteria in both Riemann-Liouville and Caputo cases. Besides, numerical examples for applicability our results.

Abstract In this paper, using necessary and sufficient conditions, the new concept of Stepanov µ -pseudo almost automorphic functions ergodicity results, we investigate existence mild bounded solutions for a class fractional integro-differential equations in sense Weyl derivative Banach space.

In this work, an algorithm for finding numerical solutions of linear fractional delay-integro-differential equations (LFDIDEs) variable-order (VO) is introduced. The operational matrices are used as discretization technique based on shifted Chebyshev polynomials (SCPs) the first kind with spectral collocation method. proposed VO-LFDIDEs have multiterms integer, fractional-order derivatives dela...

In some real world problems, fractional-order models are found to be more adequate than integer-order models. Fractional derivatives provide an excellent tool for the description of memory and hereditary properties of various materials and processes. The mathematical modelling of systems and processes in the fields of physics, chemistry, aerodynamics, electro dynamics of complex medium, polymer...

Semilinear stochastic evolution equations with multiplicative Poisson noise and monotone nonlinear drift in Hilbert spaces are considered‎. ‎The coefficients are assumed to have linear growth‎. ‎We do not impose coercivity conditions on coefficients‎. ‎A novel method of proof for establishing existence and uniqueness of the mild solution is proposed‎. ‎Examples on stochastic partial differentia...