Summary
Dr. Mujeeb ur Rehman earned a doctoral degree in Mathematics from the National University of Sciences and Technology, where he currently serves as a Professor in the Department of Mathematics at NUST School of Natural Sciences. His research focuses on areas such as Fractional Calculus, Transform Methods in Fractional Calculus, Numerical Methods for Fractional Differential Equations, and Qualitative Theory of Fractional Differential Equations.
Academic Background
PhD
(Differential Equations) NUST, Islamabad
January 04, 2008 - November 17, 2011
Honours and Awards
Best Teacher Award 2019
Best Teacher Award (2019)
December 03, 2020
Publications
On Fractional Sturm-Liouville Problem With Prabhakar Fractional Derivative
January 15, 2026
Mathematical Methods in the Applied Sciences - Volume:49, Issue:1, Pages 353-365
A generalized Legendre transform method and its applications
November 01, 2025
Journal of Computational and Applied Mathematics - Volume: 468, Article Number: 116646,
On the generalised Erdélyi–Kober fractional operators
October 15, 2025
Computational and Applied Mathematics - Volume 45, Article Number 66
On general tempered fractional calculus with Luchko kernels
April 01, 2025
Journal of Computational and Applied Mathematics - Volume:458, ID:116339
On Weighted Fractional Calculus With Respect to Functions
December 16, 2024
Mathematical Methods in the Applied Sciences - Volume:48, Issue:05, Pages:5642-5659
Solution of fractional Sturm–Liouville problems by generalized polynomials
December 09, 2024
Engineering Computations (Swansea, Wales) - Pages 1-30
A new scheme for the solution of the nonlinear Caputo–Hadamard fractional differential equations
October 01, 2024
Alexandria Engineering Journal - Volume: 105, Pages 56-69
Numerical Technique based on Generalized Laguerre and Shifted Chebyshev Polynomials
August 04, 2024
Journal of Applied Analysis and Computation - Volume 14, Number 4, Pages 1977-2001
A numerical method for solutions of tempered fractional differential equations
June 01, 2024
Journal of Computational and Applied Mathematics - Volume 443, Article Number 115772
A product integration method for numerical solutions of fractional differential equations
March 01, 2024
Journal of Computational Science - Volume 76, Article Number: 102234
A numerical technique based on multiplicative integration strategy for fractional Darboux problem
December 13, 2023
Numerical Algorithms - Pages 1-27
A numerical method for fractional Sturm–Liouville problems involving the Cauchy–Euler operators
September 01, 2023
Computational and Applied Mathematics - Volume 429, Article Number 115221
On the fractional Fourier transforms with respect to functions and its applications
June 18, 2023
Computational and Applied Mathematics - Volume 42, Issue 5, Article Number 220
A numerical method based on quadrature rules for ψ-fractional differential equations
February 01, 2023
Computational and Applied Mathematics - Volume 419, Article Number 114684
Numerical solutions of Hadamard fractional differential equations by generalized Legendre functions
December 13, 2022
Mathematical Methods in the Applied Sciences - Pages 1-22
A Legendre-spectral method for Hadamard fractional partial differential equations
November 20, 2022
Mathematical Sciences - Pages 1-17
A generalized Taylor operational matrix method for ψ-fractional differential equations
October 17, 2022
Mathematical Methods in the Applied Sciences - Pages 1-23
Ulam’s type stability analysis of fractional difference equation with impulse: Gronwall inequality approach
September 05, 2022
Turkish Journal of Mathematics - Volume 46, Issue 7, Pages 2927-2941
ψ-Shifted Operational Matrix Scheme for Fractional Partial Differential Equations
March 28, 2022
Journal of Applied Analysis and Computation - Volume 12(2), Pages 497-516
A numerical method based on Haar wavelets for the Hadamard-type fractional differential equations
March 04, 2022
Engineering Computations - Volume 39 No. 3, Pages 943-964
Generalized Mellin transform and its applications in fractional calculus
March 04, 2022
Computational and Applied Mathematics - Volume 41, Issue 3, Article Number 88
Solution of fractional boundary value problems by ψ-shifted operational matrices
January 24, 2022
AIMS Mathematics - Volume 7(4), Pages 6669-6693.
On the Existence and Ulam–Hyers Stability of a New Class of Partial (φ, χ)−Fractional Differential Equations With Impulses
November 20, 2021
Filomat - Volume 35(6), Pages 1977-1991
On Laplace transforms with respect to functions and their applications to fractional differential equations
September 12, 2021
Mathematical Methods in the Applied Sciences - Volume:46, Issue:07, Pages:8304-8323, 15 May 2023
Existence of weak solutions for ψ-caputo fractional boundary value problem via variational methods
August 01, 2021
Journal of Applied Analysis and Computation - Volume 11, Number 4, Pages 1768–1778
Tempered and Hadamard-Type Fractional Calculus with Respect to Functions
June 02, 2021
Mediterranean Journal of Mathematics - Volume 18, Article Number: 143
Ulam–Hyers–Mittag–Leffler stability of fractional difference equations with delay
June 01, 2021
Rocky Mountain Journal of Mathematics - Volume 51(3), Pages 891-901
Langevin equation with nonlocal boundary conditions involving a ψ-Caputo fractional operators of different orders
April 21, 2021
AIMS Mathematics - Volume 6, Issue 7, Pages 6749-6780
Discrete Version of Gronwall-Bellman Type Inequality and its Application in Stability Analysis
March 15, 2021
Dynamic Systems and Applications - Volume 30, No.3, Pages 449-459
Fractional Gegenbauer wavelets operational matrix method for solving nonlinear fractional differential equations
February 04, 2021
Mathematical Sciences - Pages 1-15
Stability analysis of p-laplacian fractional difference equation
January 01, 2021
Dynamic Systems and Applications - Volume 30, Issue 1, Pages 17-31
Fixed point theorem combined with variational methods for a class of nonlinear impulsive fractional problems with derivative dependence
December 04, 2020
AIMS Mathematics - Volume 6(2), Pages 1943–1953
Green–Haar wavelets method for generalized fractional differential equations
September 22, 2020
Advances in Difference Equations - Volume 2020, Article Number: 515
Generalized Substantial Fractional Operators and Well-Posedness of Cauchy Problem
September 21, 2020
Bulletin of the Malaysian Mathematical Sciences Society - Pages 1-24
Discrete fractional order two-point boundary value problem with some relevant physical applications
September 16, 2020
Journal of Inequalities and Applications - Volume 2020, Article Number 221
ψ-Haar wavelets method for numerically solving fractional differential equations
August 12, 2020
Engineering Computations - Volume 38, Issue 2, Pages 1037-1056
Green’s functions for boundary value problems of generalized fractional differential equations with p-Laplacian
August 06, 2020
Hacettepe Journal of Mathematics and Statistics - Volume 49(4), Pages 1355–1372
A Transformation Method for Delta Partial Difference Equations on Discrete Time Scale
July 10, 2020
Mathematical Problems in Engineering - Volume 2020, Article ID 3902931, 14 pages
Construction of fixed point operators for nonlinear difference equations of non integer order with impulses
June 25, 2020
Fractional Calculus and Applied Analysis - Volume 23(3), Pages 886-907
On fractional difference Langevin equations Involving non-local boundary conditions
May 29, 2020
Dynamic Systems and Applications - Volume 29, No. 2, Pages 305-326
On Caputo modification of Hadamard-type fractional derivative and fractional Taylor series
May 15, 2020
Advances in Difference Equations - Volume 2020, Article Number 219
Stability analysis by fixed point theorems for a class of non-linear Caputo nabla fractional difference equation
May 13, 2020
Advances in Difference Equations - Volume 2020, Article Number 209
Green-Haar method for fractional partial differential equations
April 16, 2020
Engineering Computations - Volume 37, Issue 4, Pages 1473-1490
On substantial fractional difference operator
April 09, 2020
Advances in Difference Equations - Volume 2020, Article Number 154
On Hilfer fractional difference operator
March 16, 2020
Advances in Difference Equations - Volume 2020, Article Number 122
Ulam-Hyers-Rassias Stability and Existence of Solutions to Nonlinear Fractional Difference Equations with Multipoint Summation Boundary Condition
March 01, 2020
Acta Mathematica Scientia - Volume 40B(2), Pages 589–602
Existence of solution of an infinite system of generalized fractional differential equations by Darbo’s fixed point theorem
January 15, 2020
Journal of Computational and Applied Mathematics - Volume 364, Article Number 112355
On the existence of positive solutions for generalized fractional boundary value problems
December 06, 2019
Boundary Value Problems - Volume: 2019, Issue: 1, Article Number: 186
Approximate Solutions for Fractional Boundary Value Problems via Green-CAS Wavelet Method
December 02, 2019
Mathematics - Vol.7(12), Article Number 1164
Ulam stability of Caputo q-fractional delay difference equation: q-fractional Gronwall inequality approach
November 29, 2019
Journal of Inequalities and Applications - Volume: 2019, Issue: 1, Article Number: 305
On oscillatory and nonoscillatory behavior of solutions for a class of fractional order differential equations
May 29, 2019
TURKISH JOURNAL OF MATHEMATICS - Volume 43, Pages 1182-1194
A numerical method for solving fractional differential equations
March 11, 2019
Engineering Computations - Volume 36, Issue 2, Pages 551-568
Ulam-Hyers-Stability for nonlinear fractional neutral differential equations
February 01, 2019
Hacettepe Journal of Mathematics and Statistics - Volume 48, Issue 1, Pages 157-169
Differential quadrature method for nonlinear fractional partial differential equations
October 17, 2018
Engineering Computations - Volume 35, Issue 6, Pages 2349-2366
On variational methods to non-instantaneous impulsive fractional differential equation
September 05, 2018
Applied Mathematics Letters - NULL
Ulam-Hyers-Mittag-Leffler stability for nonlinear fractional neutral differential equations
September 01, 2018
Sbornik Mathematics - Volume: 209, Issue: 9, Pages 1337-1350
Existence And Stability Analysis By Fixed Point Theorems For A Class Of Non-Linear Caputo Fractional Differential Equations
June 07, 2018
Dynamic Systems and Applications - -
Existence results for hybrid fractional neutral differential equations
November 02, 2017
Advances in Difference Equations - Volume 2017, Article Number: 353
On existence of positive solutions for a class of discrete fractional boundary value problems
September 03, 2017
Positivity - -
A quadrature method for numerical solutions of fractional differential equations
August 15, 2017
Applied Mathematics and Computation - Volume 307, Pages 38-49
A note on fractional Duhamel's principle and its application to a class of fractional partial differential equations
February 02, 2017
Applied Mathematics Letters - Volume: 64, Pages: 8-14
Boundary value problem for nonlinear fractional differential equations with delay
January 25, 2017
Advances in Difference Equations - Volume 2017, Issue 1, Article Number 24
A note on terminal value problems for fractional differential equations on infinite interval
February 01, 2016
Applied Mathematics Letters - Volume 52, Pages 118-125
Gegenbauer wavelets operational matrix method for fractional differential equations
September 01, 2015
Journal of the Korean Mathematical Society - Volume: 52, Issue: 5, Pages: 1069-1096
Modified Chebyshev wavelet methods for fractional delay-type equations
August 01, 2015
Applied Mathematics and Computation - Volume 264, Pages 431-442
Haar wavelet Picard method for fractional nonlinear partial differential equations
August 01, 2015
Applied Mathematics and Computation - Volume: 264, Pages: 310-322
Haar wavelet operational matrix method for fractional oscillation equations
July 15, 2014
International Journal of Mathematics and Mathematical Sciences - Volume 2014, Article ID 174819, 8 pages
Hermite Wavelet Method for Fractional Delay Differential Equations
July 02, 2014
Journal of Difference Equations - Volume 2014, Article ID: 359093
Haar Wavelet-Picard technique for fractional order nonlinear initial and boundary value problems
June 30, 2014
Scientific Research and Essays - Volume 9(12), Pages 571-580
Wavelet-Galerkin Quasilinearization Method for Nonlinear Boundary Value Problems
June 16, 2014
Abstract and Applied Analysis - Volume 2014, Article ID 868934, 10 pages
Assessment of Haar wavelet-quasilinearization technique in heat convection-radiation equations
February 05, 2014
Applied Computational Intelligence and Soft Computing - Volume 2014, Article ID 454231, 5 Pages
Haar Wavelet-Picard Technique for Factional Order Nonlinear Initial and Boundary Value Problems
January 01, 2014
Scientific Research and Essays - Vol. 12, Issue 9, Pages 571-580, June 2014
Existence and uniqueness of solutions for impulsive fractional differential equations
November 01, 2013
Applied Mathematics and Computation - Volume 224, Pages 422-431
Haar wavelet-quasilinearization technique for fractional nonlinear differential equations
September 01, 2013
Applied Mathematics and Computation - Volume: 220, Pages: 630-648
Numerical solutions to initial and boundary value problems for linear fractional partial differential equations
April 01, 2013
Applied Mathematical Modelling - Volume 37, Pages 5233-5244
A numerical method for solving boundary value problems for fractional differential equations
March 01, 2012
Applied Mathematical Modelling - Volume: 36, Issue: 3, Pages: 894-907
The Legendre wavelet method for solving fractional differential equations
November 01, 2011
Communications in Nonlinear Science and Numerical Simulation - Volume 16, Issue 11, Pages 4163-4173
Positive Solutions of Nonlocal Boundary Value Problem for Higher Order Fractional Differential System
September 01, 2011
Dynamic Systems and Applications - Volume: 20, Issue: 2-3, Pages: 169-182
Three point boundary value problems for nonlinear fractional differential equations
July 01, 2011
Acta Mathematica Scientia - Volume 31, Issue 4, Pages 1337-1346
A note on boundary value problems for a coupled system of fractional differential equations
May 02, 2011
Computers and Mathematics with Applications - Volume 61, Issue 9, Pages 2630-2637
Positive Solutions to Nonlinear Higher-Order Nonlocal Boundary Value Problems for Fractional Differential Equations
October 28, 2010
Abstract and Applied Analysis - Article Number 501230
Existence and uniqueness of solutions for multi-point boundary value problem for fractional differential equations
September 01, 2010
Applied Mathematics Letters - Volume: 23, Issue: 9, Pages: 1038-1044