.github/workflows/Benchmark.yml

@@ -0,0 +1,55 @@
+name: Benchmarks
+on:
+  push:
+    branches:
+      - master
+  pull_request:
+    branches:
+      - master
+
+concurrency:
+  # Skip intermediate builds: always.
+  # Cancel intermediate builds: only if it is a pull request build.
+  group: ${{ github.workflow }}-${{ github.ref }}
+  cancel-in-progress: ${{ startsWith(github.ref, 'refs/pull/') }}
+
+jobs:
+  benchmark:
+    runs-on: ubuntu-latest
+    steps:
+      - uses: actions/checkout@v4
+      - uses: julia-actions/setup-julia@v1
+        with:
+          version: '1'
+          arch: x64
+      - uses: actions/cache@v4
+        env:
+          cache-name: cache-artifacts
+        with:
+          path: ~/.julia/artifacts
+          key: ${{ runner.os }}-test-${{ env.cache-name }}-${{ hashFiles('**/Project.toml') }}
+          restore-keys: |
+            ${{ runner.os }}-test-${{ env.cache-name }}-
+            ${{ runner.os }}-test-
+            ${{ runner.os }}-
+      - name: Run benchmark
+        run: |
+          cd bench
+          julia --project --color=yes -e '
+            using Pkg;
+            Pkg.develop(PackageSpec(path=joinpath(pwd(), "..")));
+            Pkg.instantiate();
+            include("runbenchmarks.jl")'
+      - name: Parse & Upload Benchmark Results
+        uses: benchmark-action/github-action-benchmark@v1
+        with:
+          name: Benchmark Results
+          tool: 'julia'
+          output-file-path: bench/benchmark_results.json
+          summary-always: true
+          github-token: ${{ secrets.GITHUB_TOKEN }}
+          comment-always: true
+          alert-threshold: "200%"
+          fail-on-alert: true
+          benchmark-data-dir-path: benchmarks
+          auto-push: ${{ github.event_name != 'pull_request' }}

.github/workflows/CI.yml

@@ -10,8 +10,8 @@ jobs:
       fail-fast: false
       matrix:
         version:
-          - '1.6'
-          - 'nightly'
+          - '1'
+          - '~1.10.0-0'
         os:
           - ubuntu-latest
           - macOS-latest

.gitignore

@@ -24,4 +24,6 @@ docs/site/
 # It records a fixed state of all packages used by the project. As such, it should not be
 # committed for packages, but should be committed for applications that require a static
 # environment.
-Manifest.toml
+Manifest.toml
+
+bench/benchmark_results.json

Project.toml

@@ -2,21 +2,29 @@ name = "FractionalCalculus"
 uuid = "638fb199-4bb2-4014-80c8-6dc0d90f156b"
 license = "MIT"
 authors = ["Qingyu Qu <erikqqy123@gmail.com>"]
-version = "0.2.4"
+version = "0.3.0"
 
 [deps]
+ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
 InvertedIndices = "41ab1584-1d38-5bbf-9106-f11c6c58b48f"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 QuadGK = "1fd47b50-473d-5c70-9696-f719f8f3bcdc"
 SpecialFunctions = "276daf66-3868-5448-9aa4-cd146d93841b"
 SpecialMatrices = "928aab9d-ef52-54ac-8ca1-acd7ca42c160"
+SymbolicUtils = "d1185830-fcd6-423d-90d6-eec64667417b"
+Symbolics = "0c5d862f-8b57-4792-8d23-62f2024744c7"
+UnPack = "3a884ed6-31ef-47d7-9d2a-63182c4928ed"
 
 [compat]
-InvertedIndices = "1.1"
-QuadGK = "2.4.2"
-SpecialFunctions = "1.6.2, 2"
-SpecialMatrices = "2.0.0"
-julia = "1.0"
+ForwardDiff = "0.10.36"
+InvertedIndices = "1.3"
+QuadGK = "2.9"
+SpecialFunctions = "2.3"
+SpecialMatrices = "3"
+SymbolicUtils = "1.5"
+Symbolics = "5.13"
+UnPack = "1.0.2"
+julia = "1.9"
 
 [extras]
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"

README.md

@@ -1,11 +1,5 @@
 # FractionalCalculus.jl
 
-<p align="center">
-<img width="250px" src="https://raw.githubusercontent.com/SciFracX/FractionalCalculus.jl/master/docs/src/assets/logo.svg"/>
-</p>
-
-
-<p align="center">
   <a href="https://github.com/SciFracX/FractionalCalculus.jl/actions?query=workflow%3ACI">
     <img alt="building" src="https://github.com/SciFracX/FractionalCalculus.jl/workflows/CI/badge.svg">
   </a>
@@ -21,9 +15,6 @@
     <a href="https://zenodo.org/badge/latestdoi/420992306">
   	<img src="https://zenodo.org/badge/420992306.svg" alt="DOI">
   </a>
-</p>
-
-<p align="center">
   <a href="https://github.com/SciFracX/FractionalCalculus.jl/issues">
     <img alt="GitHub issues" src="https://img.shields.io/github/issues/SciFracX/FractionalCalculus.jl?style=flat-square">
   </a>
@@ -33,43 +24,36 @@
   <a href="https://github.com/SciFracX/FractionalCalculus.jl/network">
     <img alt="GitHub forks" src="https://img.shields.io/github/forks/SciFracX/FractionalCalculus.jl?style=flat-square">
   </a>
-</p>
 
 FractionalCalculus.jl provides support for fractional calculus computing.
 
 ## 🎇 Installation
 
-If you have already install Julia, you can install FractionalCalculus.jl in REPL using Julia package manager:
+If you have already installed Julia, you can install FractionalCalculus.jl in REPL using Julia package manager:
 
 ```julia
 pkg> add FractionalCalculus
 ```
 
-Or if you want to experience the latest version of FractionalCalculus.jl:
-
-```julia
-pkg> add FractionalCalculus#master
-```
-
 ## 🦸 Quick start
 
 ### Derivative
 
-To compute the fractional derivative in a specific point, for example, compute <img src="https://latex.codecogs.com/svg.image?\inline&space;\alpha=0.2" title="\inline \alpha=0.2" /> derivative of <img src="https://latex.codecogs.com/svg.image?\inline&space;f(x)=x" title="\inline f(x)=x" /> in <img src="https://latex.codecogs.com/svg.image?\inline&space;x=1" title="\inline x=1" /> with step size <img src="https://latex.codecogs.com/svg.image?\inline&space;h=0.0001" title="\inline h=0.0001" /> using **Riemann Liouville** sense:
+To compute the fractional derivative in a specific point, for example, compute $\alpha = 0.2$ derivative of $f(x) = x$ in $x = 1$ with step size $h = 0.0001$ using **Riemann Liouville** sense:
 
 ```julia
-julia> fracdiff(x->x, 0.2, 1, 0.0001, RLDiff_Approx())
+julia> fracdiff(x->x, 0.2, 1, 0.0001, RLDiffL1())
 1.0736712740308347
 ```
 
 This will return the estimated value with high precision.
 
 ### Integral
 
-To compute the fractional integral in a specific point, for example, compute the semi integral of <img src="https://latex.codecogs.com/svg.image?\inline&space;f(x)=x" title="\inline f(x)=x" /> in <img src="https://latex.codecogs.com/svg.image?\inline&space;x=1" title="\inline x=1" />  with step size <img src="https://latex.codecogs.com/svg.image?\inline&space;h=0.0001" title="\inline h=0.0001" /> using **Riemann-Liouville** sense:
+To compute the fractional integral in a specific point, for example, compute the semi integral of $f(x) = x$ in $x = 1$  with step size $h = 0.0001$ using **Riemann-Liouville** sense:
 
 ```julia
-julia> fracint(x->x, 0.5, 1, 0.0001, RLInt_Approx())
+julia> fracint(x->x, 0.5, 1, 0.0001, RLIntApprox())
 0.7522525439593486
 ```
 
@@ -81,64 +65,81 @@ This will return the estimated value with high precision.
 Current Algorithms
 ├── FracDiffAlg
 │   ├── Caputo
-|   |   ├── Caputo_Direct
-|   |   ├── Caputo_Piecewise
-|   |   ├── Caputo_Diethelm
-|   |   └── Caputo_High_Precision
+|   |   ├── CaputoDirect
+|   |   ├── CaputoTrap
+|   |   ├── CaputoDiethelm
+|   |   ├── CaputoHighPrecision
+|   |   ├── CaputoL1
+|   |   ├── CaputoL2
+|   |   └── CaputoHighOrder
 |   |
 │   ├── Grünwald Letnikov
-|   |   ├── GL_Direct
-|   |   ├── GL_Multiplicative_Additive
-|   |   ├── GL_Lagrange_Three_Point_Interp
-|   |   └── GL_High_Precision
+|   |   ├── GLDirect
+|   |   ├── GLMultiplicativeAdditive
+|   |   ├── GLLagrangeThreePointInterp
+|   |   └── GLHighPrecision
 |   |
 |   ├── Riemann Liouville
-|   |    ├── RLDiff_Approx
-|   |    ├── RL_Linear_Spline_Interp
-|   |    ├── RLDiff_Matrix
-|   |    ├── RL_G1
-|   |    └── RL_D
+|   |    ├── RLDiffL1
+|   |    ├── RLDiffL2
+|   |    ├── RLDiffL2C
+|   |    ├── RLLinearSplineInterp
+|   |    ├── RLDiffMatrix
+|   |    ├── RLG1
+|   |    └── RLD
 |   | 
 |   ├── Hadamard
-|   |    ├── Hadamard_LRect
-|   |    ├── Hadamard_RRect
-|   |    └── Hadamard_Trap
+|   |    ├── HadamardLRect
+|   |    ├── HadamardRRect
+|   |    └── HadamardTrap
+|   |
+|   ├── Riesz
+|   |    ├── RieszSymmetric
+|   |    └── RieszOrtigueira
+|   |
+|   ├── Caputo-Fabrizio
+|   |    └── CaputoFabrizioAS
 |   |
-|   └── Riesz
-|        └── Riesz_Symmetric
+|   └── Atanagana Baleanu
+|        └── AtanganaSeda
 |
 └── FracIntAlg
-    └── Riemann Liouville
-        ├── RL_Direct
-        ├── RL_Piecewise
-        ├── RL_LinearInterp
-        ├── RLInt_Approx
-        ├── RLInt_Matrix
-        ├── RLInt_Simpson
-        ├── RLInt_Trapezoidal
-        ├── RLInt_Rectangular
-        └── RLInt_Cubic_Spline_Interp
+    ├── Riemann Liouville
+    |   ├── RLDirect
+    |   ├── RLPiecewise
+    |   ├── RLLinearInterp
+    |   ├── RLIntApprox
+    |   ├── RLIntMatrix
+    |   ├── RLIntSimpson
+    |   ├── RLIntTrapezoidal
+    |   ├── RLIntRectangular
+    |   └── RLIntCubicSplineInterp
+    |
+    └── Hadamard
+        └── HadamardMat
 ```
 
+For detailed usage, please refer to [our manual](https://scifracx.org/FractionalCalculus.jl/dev/Derivative/derivativeapi/).
+
 ## 🖼️ Example
 
 Let's see examples here:
 
-Compute the semi-derivative of <img src="https://latex.codecogs.com/svg.image?\inline&space;f(x)=x" title="\inline f(x)=x" /> in the interval <img src="https://latex.codecogs.com/svg.image?[0,\&space;1]" title="[0,\ 1]" />:
+Compute the semi-derivative of $f(x) = x$ in the interval $\left[0, 1\right]$:
 
 ![Plot](/docs/src/assets/semiderivativeplot.png)
 
-We can see the computing retains high precision⬆️.
+We can see that computing retains high precision⬆️.
 
-Compute different order derivative of <img src="https://latex.codecogs.com/svg.image?\inline&space;f(x)=x" title="\inline f(x)=x" />:
+Compute different order derivative of $f(x) = x$:
 
 ![Different Order](/docs/src/assets/different_order_x_derivative.png)
 
-Also different order derivative of <img src="https://latex.codecogs.com/svg.image?\inline&space;f(x)=\sin(x)" title="\inline f(x)=\sin(x)" />:
+Also different order derivative of $f(x) = \sin(x)$:
 
 ![Different Order of sin](/docs/src/assets/different_order_sin_derivative.png)
 
-And also different order integral of <img src="https://latex.codecogs.com/svg.image?\inline&space;f(x)=x" title="\inline f(x)=x" />:
+And also different order integral of $f(x) = x$:
 
 ![Different Order Of x](/docs/src/assets/different_order_x_integral.png)
 
@@ -150,6 +151,19 @@ Or arbitrary order derivative? A piece of cake!!😉
 
 -->
 
+## 🧙 Symbolic Fractional Differentiation and Integration
+
+Thanks to SymbolicUtils.jl, FractionalCalculus.jl can do symbolic fractional differentiation and integration now!!
+
+```julia
+julia> using FractionalCalculus, SymbolicUtils
+julia> @syms x
+julia> semidiff(log(x))
+log(4x) / sqrt(πx)
+julia> semiint(x^4)
+0.45851597901024005(x^4.5)
+```
+
 ## 📢 Status
 
 Right now, FractionalCalculus.jl has only supports for little algorithms:
@@ -161,22 +175,18 @@ Fractional Derivative:
 - [x] Riemann-Liouville fractional derivative 
 - [x] Riesz fractional derivative
 - [x] Hadamard  fractional derivative
-- [ ] Caputo-Fabrizio fractional derivative
-- [ ] Atangana-Baleanu fractional derivative
+- [x] Caputo-Fabrizio fractional derivative
+- [x] Atangana-Baleanu fractional derivative
 - [ ] Marchaud fractional derivative
-- [ ] Weyl  fractional derivative
+- [ ] Weyl fractional derivative
 - [ ] ......
 
 Fractional Integral:
 - [x] Riemann-Liouville fractional integral
-- [ ] Hadamard fractional integral
+- [x] Hadamard fractional integral
 - [ ] Atangana-Baleanu fractional integral
 - [ ] ......
 
-## 🧙 About Symbolic differentiation and integration
-
-I am trying to find a way to support symbolic differentiation and integration features🤔.
-
 ## 📚 Reference
 
 FractionalCalculus.jl is built upon the hard work of many scientific researchers, I sincerely appreciate what they have done to help the development of science and technology.

bench/.JuliaFormatter.toml

@@ -0,0 +1,9 @@
+style = "sciml"
+whitespace_in_kwargs = false
+always_use_return = true
+margin = 92
+indent = 4
+format_docstrings = true
+separate_kwargs_with_semicolon = true
+always_for_in = true
+annotate_untyped_fields_with_any = false

bench/Project.toml

@@ -0,0 +1,4 @@
+[deps]
+BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
+FractionalCalculus = "638fb199-4bb2-4014-80c8-6dc0d90f156b"
+Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"

bench/README.md

@@ -0,0 +1,6 @@
+# FractionalCalculus.jl Continuous Benchmarking
+
+Currently, we use the BenchmarkTools.jl package to benchmark the performance of FractionalCalculus.jl over time.
+
+This is built using https://github.com/benchmark-action/github-action-benchmark/ so it
+allows for nice visualizations of the benchmark results in github pages and produces warnings on PRs if the benchmarks regress.

bench/derivative.jl

@@ -0,0 +1,9 @@
+function benchmark_caputo(tag::String, end_tag::String, step_size::Real)
+    SUITE["fracdiff"]["cpu"][tag][end_tag] = @benchmarkable fracdiff(x->x^2, 0.5, 1, $step_size, CaputoDiethelm())
+    SUITE["fracdiff"]["cpu"][tag][end_tag] = @benchmarkable fracdiff(x->x^2, 0.5, 1, $step_size, CaputoL1())
+end
+
+function benchmark_RL(tag::String, end_tag::String, step_size::Real)
+    SUITE["fracdiff"]["cpu"][tag][end_tag] = @benchmarkable fracdiff(x->x^2, 0.5, 1, $step_size, RLD())
+    SUITE["fracdiff"]["cpu"][tag][end_tag] = @benchmarkable fracdiff(x->x^2, 0.5, 1, $step_size, RLDiffL1())
+end