Fractional Differential Equations Associated with Generalized Fractional Operators in $F_{p,\upnu}$ Space

Manish Kumar Bansal, Priyanka Harjule, Devendra Kumar

Abstract

The key aim of the present work is to study the fractional differential equations (FDEs) pertaining to generalized fractional operators in $F_{p,\upnu}$ space. First, we derive the Laplace transform of the generalized fractional operators in terms of generalized modified Bessel function type transform $ \mathbb{L}_{\upalpha,\upbeta}^{(\upsigma)} $ in $ F_{p,\upnu} $ space. The results obtained are used to  solve the FDEs involving constant as well as variable coefficients in $ F_{p,\upnu} $ space. Due to the general nature of M-S-M integral operators many new and useful special cases of the key results can be obtained.