On Hilfer generalized proportional fractional derivative

[1]  P. Kumam,et al.  Stability analysis for boundary value problems with generalized nonlocal condition via Hilfer–Katugampola fractional derivative , 2020 .

[2]  A. Atangana,et al.  LOCAL AND NONLOCAL DIFFERENTIAL OPERATORS: A COMPARATIVE STUDY OF HEAT AND MASS TRANSFERS IN MHD OLDROYD-B FLUID WITH RAMPED WALL TEMPERATURE , 2020 .

[3]  A. Atangana,et al.  CAUCHY PROBLEMS WITH FRACTAL–FRACTIONAL OPERATORS AND APPLICATIONS TO GROUNDWATER DYNAMICS , 2020 .

[4]  Abdon Atangana,et al.  Modelling and analysis of fractal-fractional partial differential equations: Application to reaction-diffusion model , 2020 .

[5]  Abdon Atangana,et al.  Modeling the dynamics of novel coronavirus (2019-nCov) with fractional derivative , 2020, Alexandria Engineering Journal.

[6]  K. Shah,et al.  Stability Results for Implicit Fractional Pantograph Differential Equations via ϕ-Hilfer Fractional Derivative with a Nonlocal Riemann-Liouville Fractional Integral Condition , 2020, Mathematics.

[7]  H. Alzumi,et al.  Existence results for nonlinear fractional boundary value problem involving generalized proportional derivative , 2019, Advances in Difference Equations.

[8]  Poom Kumam,et al.  Nonlinear Caputo Fractional Derivative with Nonlocal Riemann-Liouville Fractional Integral Condition Via Fixed Point Theorems , 2019, Symmetry.

[9]  D. S. Oliveira,et al.  Hilfer–Katugampola fractional derivatives , 2018 .

[10]  K. Shah,et al.  Note on the solution of random differential equations via ψ-Hilfer fractional derivative , 2018, Advances in Difference Equations.

[11]  K. Kanagarajan,et al.  Some Existence and Stability Results for Hilfer-fractional Implicit Differential Equations with Nonlocal Conditions , 2018 .

[12]  T. Abdeljawad,et al.  Generalized fractional derivatives generated by a class of local proportional derivatives , 2017 .

[13]  D. Baleanu,et al.  On a new class of fractional operators , 2017 .

[14]  Abdon Atangana,et al.  New direction in fractional differentiation , 2017 .

[15]  Dumitru Baleanu,et al.  On the generalized fractional derivatives and their Caputo modification , 2017 .

[16]  A. Atangana,et al.  Application of fixed point theorem for stability analysis of a nonlinear Schrodinger with Caputo-Liouville derivative , 2017 .

[17]  Ricardo Almeida,et al.  A Caputo fractional derivative of a function with respect to another function , 2016, Commun. Nonlinear Sci. Numer. Simul..

[18]  A. Alsaedi,et al.  New properties of conformable derivative , 2015 .

[19]  Abdon Atangana,et al.  Derivative with a New Parameter: Theory, Methods and Applications , 2015 .

[20]  Thabet Abdeljawad,et al.  On conformable fractional calculus , 2015, J. Comput. Appl. Math..

[21]  M. Sababheh,et al.  A new definition of fractional derivative , 2014, J. Comput. Appl. Math..

[22]  D. Baleanu,et al.  On Caputo modification of the Hadamard fractional derivatives , 2014 .

[23]  A. Atangana,et al.  A Note on Fractional Order Derivatives and Table of Fractional Derivatives of Some Special Functions , 2013 .

[24]  Nasser-eddine Tatar,et al.  Existence and uniqueness for a problem involving Hilfer fractional derivative , 2012, Comput. Math. Appl..

[25]  D. Baleanu,et al.  Caputo-type modification of the Hadamard fractional derivatives , 2012 .

[26]  Udita N. Katugampola A NEW APPROACH TO GENERALIZED FRACTIONAL DERIVATIVES , 2011, 1106.0965.

[27]  Udita N. Katugampola New approach to a generalized fractional integral , 2010, Appl. Math. Comput..

[28]  F. Mainardi Fractional Calculus and Waves in Linear Viscoelasticity: An Introduction to Mathematical Models , 2010 .

[29]  H. Srivastava,et al.  Theory and Applications of Fractional Differential Equations, Volume 204 (North-Holland Mathematics Studies) , 2006 .

[30]  R. Hilfer Applications Of Fractional Calculus In Physics , 2000 .

[31]  Thomas J. Osler,et al.  The Fractional Derivative of a Composite Function , 1970 .

[32]  K. Shah,et al.  Dynamics and stability of ψ-fractional pantograph equations with boundary conditions , 2021 .

[33]  T. Abdeljawad,et al.  Generalized fractional derivatives and Laplace transform , 2020, Discrete & Continuous Dynamical Systems - S.

[34]  K. Shah,et al.  Existence and stability results to a class of fractional random implicit differential equations involving a generalized Hilfer fractional derivative , 2020, Discrete & Continuous Dynamical Systems - S.

[35]  S. Harikrishnan,et al.  Dynamics and stability of Hilfer-Hadamard type fractional pantograph equations with boundary conditions , 2018 .

[36]  D. Anderson Self-Adjoint Differential Equations Using a Proportional-Derivative Controller , 2017 .

[37]  D. Anderson,et al.  Newly Defined Conformable Derivatives , 2015 .

[38]  R. Magin Fractional Calculus in Bioengineering , 2006 .

[39]  R. Feynman,et al.  RECENT APPLICATIONS OF FRACTIONAL CALCULUS TO SCIENCE AND ENGINEERING , 2003 .

[40]  Anatoly A. Kilbas,et al.  HADAMARD-TYPE FRACTIONAL CALCULUS , 2001 .

[41]  I. Podlubny Fractional differential equations : an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications , 1999 .